The candidates mostly tempered their criticism of one another and presented a united front on vital issues like climate change.

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Ten presidential candidates took the stage in Atlanta to discuss topics including impeachment, climate change and foreign policy. Also, there were some jokes.CreditCredit...Ruth Fremson/The New York Times

The Democratic presidential candidates yielded to the furor surrounding the impeachment inquiry in Washington in their primary debate on Wednesday, for the first time training their fire more steadily on President Trump than on one another and presenting a largely united front on vital issues like climate change and abortion rights.

One month after the party’s moderate wing led a ferocious attack against Senator Elizabeth Warren of Massachusetts at the previous debate, the leading Democrats opted to mute their rivalries and restrain their language, mainly detailing their disagreements in gentle or at most passive-aggressive terms. There were moments of direct friction, especially in the final minutes of the debate over matters of national security, but in many cases the candidates’ criticism was couched within jocular one-liners or pragmatic arguments about electability.

Most telling were a handful of sharper exchanges among the 10 candidates onstage in Atlanta related to matters of race and gender. Several expressed concerns about the prospect of nominating a white man, like former Vice President Joseph R. Biden Jr. or Mayor Pete Buttigieg of South Bend, Ind. Senators Cory Booker of New Jersey and Kamala Harris of California both warned that the party could not afford to select a candidate who was not capable of exciting African-American voters, and Ms. Harris repeatedly invoked “the Obama coalition” as the Democrats’ best hope for electoral success.

“Black voters are pissed off and they’re worried,” Mr. Booker said, lamenting that too many African-American voters hear from Democratic candidates only during election season.

He also rebuked Mr. Biden for expressing resistance last weekend to legalizing marijuana, joking, “I thought you might have been high when you said it.”

Mr. Buttigieg and Mr. Biden both insisted they were capable of marshaling support from minority voters. Mr. Buttigieg acknowledged that he faced “the challenge of connecting with black voters” who do not know him yet, and Mr. Biden argued that his present strength with African-American primary voters spoke for itself. “I was part of that coalition,” he said, even adding: “I come out of the black community.”

As for the Obama coalition, Mr. Biden once again referred his personal bond with the former president: “I was part of that coalition,” he said.

It was widely anticipated that Mr. Buttigieg would become a kind of political pin cushion onstage, as other Democrats sought to harry him as the emerging front-runner in Iowa. But it was only in the final moments of the debate that he drew sustained criticism, first from Senator Amy Klobuchar of Minnesota and then, more caustically, from Representative Tulsi Gabbard of Hawaii.

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Credit...Demetrius Freeman for The New York Times

But it is unclear whether anyone raised new doubts about the young mayor as a contender for the nation’s most powerful office. Ms. Klobuchar noted that Mr. Buttigieg, 37, had lost his only statewide election, and lacked a governing record on issues, like voting rights, that he talked about on the campaign trail. “I think experience should matter, she said.

But Mr. Buttigieg, deploying a recurring tactic of deflection, dismissed the value of experience in Washington and cited his service in the military.

Ms. Gabbard was a more persistent adversary, rebuking Mr. Buttigieg for saying in a recent interview that he might be willing to deploy American troops in Mexico to fight violence there. Mr. Buttigieg again held his ground, calling Ms. Gabbard’s characterization of his remarks “outlandish” and chiding her for having met with the “murderous dictator” Bashar al-Assad during a trip to Syria.

But for the most part, the Democrats focused on denouncing Mr. Trump. That was in part because, unlike at previous debates, the moderators avoided stoking rivalries and highlighting differences. Yet the lack of vitriol and the intense focus on electability also owed to the nature of this campaign, which as the impeachment inquiry unfolds is becoming even more centered on finding the best candidate to defeat the president.

The candidates attacked Mr. Trump both for his actions toward Ukraine that have prompted impeachment proceedings and for a longer litany of offenses, including his detention of children at the Mexican border, his warm relationships with dictatorial governments in Saudi Arabia and North Korea and his appointment of political cronies to prominent jobs in government.

The debate also highlighted the considerable areas of agreement across the Democratic field on overarching policy goals, including taking aggressive action to counter climate change, expanding voting rights and restoring traditional American alliances around the world.

Ms. Warren used the impeachment inquiry, and the testimony on Wednesday by Gordon D. Sondland, the ambassador to the European Union and a Trump donor, to criticize the practice of installing wealthy political supporters in overseas embassies. Mr. Booker railed against Mr. Trump for what he described as his human rights violations at the southern border, such as “when children are thrown in cages.”

Ms. Harris jabbed that Mr. Trump “got punked” by Kim Jong-un, the North Korean dictator, in nuclear negotiations. For Ms. Klobuchar, it was Mr. Trump’s forgiving treatment of Saudi Arabia after its agents kidnapped and killed the journalist Jamal Khashoggi.

“That sent a signal to dictators around the world that that’s O.K.,” Ms. Klobuchar said.

Still, if there were no heated moments likely to endure past the evening, as there had been in past debates, there were fault lines within the field, separating the most progressive candidates, like Ms. Warren and Senator Bernie Sanders of Vermont, from comparatively moderate figures like Mr. Biden, Mr. Buttigieg and Ms. Klobuchar.

Mr. Buttigieg, who eagerly assailed Ms. Warren’s health care policies at the debate in October, was far more veiled in his criticism this time, arguing that Democrats must “galvanize not polarize” a coalition representing a majority of voters. And Ms. Klobuchar suggested that there were candidates who were making big promises “because they sound good on a bumper sticker and then throw in a free car.” But neither of them named names or tried a direct attack as they had done last month. Similarly, Ms. Harris, whose campaign has been on a downward spiral in the polls, notably declined an opportunity to confront Mr. Buttigieg.

The leading candidates of the left took much the same approach. Mr. Sanders, defending his support for single-payer health care, referred to skeptical competitors who he said believed “that we should not take on the insurance company, we should not take on the pharmaceutical industry.” But he did not say to whom he was referring.

Mr. Sanders took only an oblique shot at Ms. Warren, who has not prioritized the measure, noting that he would introduce his single-payer system “in the first week” of his presidency.

Mr. Biden did not appear to incur new damage to his campaign, which has been durable despite some of his self-inflicted errors. Yet at a moment when a pair of new candidates were entering the race in part because of his perceived weakness, the former vice president appeared tongue-tied on more than one occasion.

He drew nervous laughter when, in discussing domestic violence, he said it was important to keep “punching at” the problem. And when he was boasting about receiving the support of the first African-American woman elected to the Senate, former Senator Carol Moseley Braun, he referred to her as the only black woman elected to the body rather than the first.

That prompted a bemused response from Ms. Harris.

“The other one is here,” she said.

Mr. Biden, who has staked his campaign on the perception that he is a strong general election candidate, focused on his broad appeal, urging Democrats to pick a nominee who could “go into states like Georgia and North Carolina and other places and get a Senate majority.”

It was, atypically, Mr. Booker, normally a nonconfrontational voice on the debate stage, who opened a more contentious phase in the first half of the debate, critiquing Ms. Warren’s proposal for a tax on the nation’s largest fortunes. “It’s cumbersome,” Mr. Booker jabbed. “It’s been tried by other nations. It’s hard to evaluate.”

The exchanges grew notably less polite, though, when Ms. Harris was offered a chance to respond on a foreign policy question that went to Ms. Gabbard, who had targeted Ms. Harris at a debate over the summer.

Ms. Harris, with payback in mind, ignored the policy element of the question and unloaded on Ms. Gabbard. She noted that her rival had been a frequent guest on Fox News, refused to call Mr. al-Assad “a war criminal” and “buddied up to Steve Bannon” during Mr. Trump’s presidential transition.

Ms. Gabbard responded that Ms. Harris was merely offering “lies and smears and innuendo” and asserted that the senator would continue the “Bush-Clinton-Trump foreign policy of regime change wars.”

Mr. Buttigieg, who is rising rapidly in the polls in Iowa, found himself for the first time in the position of defending his qualifications for the presidency. Mr. Buttigieg, who has never held statewide office, argued that from the vantage point of South Bend it was “the usual way of doing business in Washington is what looks small.”

Two of Mr. Buttigieg’s rivals pushed back more or less gently. Mr. Booker, a former mayor of Newark, described himself as “the other Rhodes scholar mayor on this stage” — perhaps his most pointed expression of feeling overlooked in the race.

But it was Ms. Klobuchar who most effectively pivoted from her past criticism of Mr. Buttigieg, whom she has described as benefiting in the race from being male, into a forceful plea to the country to elect a female president.

“Women are held to a higher standard, otherwise we could play a game called name your favorite woman president,” Ms. Klobuchar said, brandishing one of her favorite lines from the campaign trail: “If you think a woman can’t beat Donald Trump, Nancy Pelosi does it every single day.”

While she was not as pugilistic as in the last forum, Ms. Klobuchar enjoyed another series of memorable moments in this debate, including a crack about raising money from ex-boyfriends.

The businessman Andrew Yang, who has attracted a strong niche following of mostly younger voters, received little time but drew a mix of applause and laughs when he was called on. Asked what he would say, as president, in his first phone call with President Vladimir V. Putin of Russia, Mr. Yang responded: “Well, first I’d say I’m sorry I beat your guy.”

Since the debate last month, the race has become more fluid than ever; former Gov. Deval Patrick of Massachusetts has entered the primary contest, and former Mayor Michael R. Bloomberg of New York has taken steps to do the same. They have been lured into the campaign in part over their concerns about the leftward drift in the party, and also because there is still no clear front-runner with just over two months until the Iowa caucuses. It remains far from certain that they will be able to catch on so late in the race, but both have made clear that they are trying to win over more moderate voters.