LOS ALTOS HILLS, Calif. — Former President Barack Obama urged Democrats on Thursday to “chill out” about the party’s 2020 field and to avoid putting candidates through “purity tests,” and warned that average voters are “nervous about changes that might take away what little they have.”

Speaking to party donors a day after the latest Democratic primary debate, Mr. Obama added to a series of recent remarks about American politics and the presidential race, including his warning on Friday that the candidates not move too far to the left in their policy proposals and his observation that the average American does not want to “tear down the system.”

Mr. Obama’s comments on Thursday appeared at times aimed more at Democratic officials, activists and donors than at the candidates themselves. Democrats should focus less on the “tactical disagreements” among the candidates, Mr. Obama said, and avoid making false choices between appealing to white working class voters or minority voters, or between energizing the party’s base or reaching out to independents and Republicans.

“Everybody needs to chill out about the candidates, but gin up about the prospect of rallying behind” a candidate, Mr. Obama said.

“There will be differences” among the candidates, Mr. Obama said, but the ultimate goal “is to defeat a president and a party that has, I think, taken a sharp turn away from a lot of the core traditions and values and institutional commitments that built this country.”

With Democratic activists and voters now weighing the different policy ideas and positions of the candidates, Mr. Obama also warned against demanding that the party’s hopefuls meet inflexible standards.

“I’m always suspicious of purity tests during elections,” Mr. Obama said. “Because you know what? The country’s complicated.”

Mr. Obama spoke to a group of about 100 donors in Los Altos Hills, Calif., during an interview with Thomas E. Perez, the Democratic National Committee chairman, at a fund-raising event for the Democratic Unity Fund, which will be used to help the party’s eventual nominee. Aides to Mr. Obama say that it is the last time he plans to speak this year about the 2020 race.

Mr. Obama did not single out any candidates by name, and said he was encouraged that they are proposing “bolder” ideas and expanding on policies that he tried to “push the envelope” on during his administration, such as criminal justice reform.

Still, he seemed to caution against pushing for too much change.

“When you listen to the average voter — even ones who aren’t stalwart Democrats, but who are more independent or are low-information voters — they don’t feel that things are working well, but they’re also nervous about changes that might take away what little they have,” he said.

At the same time, Mr. Obama said he was open to the idea of higher taxes for the wealthy, adding that the conversation around the country has changed dramatically since his campaigns.

“I’ve got a lot of room to pay more taxes — and I already pay really high taxes,” he said. “That’s one area where I guarantee you where you will get Joe six-pack and the single inner-city mom agreeing. They would like to see a little bigger share of the pie and you know, the rent is too damn high.”

The remarks come less than a week after Mr. Obama warned against Democratic presidential candidates moving too far to the left, jockeying to win over “left-leaning Twitter feeds” rather than appealing to voters in the middle.

In recent weeks, Mr. Obama has repeatedly said that the presidential candidates should stop being concerned with debates over ideological purity and instead focus on beating President Trump.

Mr. Obama tried to “ease people’s anxieties” about his confidence in the field, saying that whoever emerges from the primary process will be a stronger candidate.

“Their flaws are magnified,” Mr. Obama said. “People are picking away: Well, you know they’re not quite this and they’re not quite that — you know it’s a natural thing.”

Many Democratic voters say they are looking for a candidate they believe is most likely to win during the general election, and there have been extensive discussions about whether that means winning over white working class voters who voted for Mr. Obama and then Mr. Trump, or turning out voters who sat out the 2016 election. Mr. Obama told donors he believed that debate was a false choice.

Mr. Perez pointed out that Mr. Obama won Iowa in 2008, suggesting that his winning coalition included both white voters as well as black and Hispanic voters.

“There aren’t a lot of black people in Iowa,” Mr. Obama said, prompting loud laughter from the donors in the room.

“At the end of the day, we are going to need everybody,” Mr. Obama said. “We will not win just by increasing the turnout of people who already agrees with us completely on everything.”

Mr. Obama also spoke about the possibility of having a female nominee — there are five women now running — or a gay nominee. (Mayor Pete Buttigieg is the first major openly gay candidate in a Democratic presidential primary.)

“Those candidates are going to have barriers if they win the nomination, if they win the general election, just like I did.” he said. “Are there going to be people in the back of their mind thinking, ‘Eh, I don’t know.’ Just like those who said I don’t know about Barack Hussein Obama.”