WASHINGTON — For Benny Gantz, the leader of the centrist Blue and White Party in Israel, traveling to Washington on Monday to meet with President Trump at the same time as the man he is trying to defeat wasn’t exactly a state visit.

While Prime Minister Benjamin Netanyahu of Israel flew a chartered El Al passenger jet to Washington, Mr. Gantz, the former Israeli military chief, flew commercial and had a three-hour layover in Zurich.

While Mr. Netanyahu was put up at Blair House, the presidential guesthouse for foreign leaders, across the street from the White House, Mr. Gantz’s team had to book him at The Jefferson, a hotel about a half-mile away.

Despite the disadvantages of traveling as a member of Parliament, rather than as a prime minister, Mr. Gantz managed to make the best of playing second fiddle to his opponent. (The two face off in their third contest on March 2.) And by showing off some unexpected political dexterity in his dealings with the White House, he avoided falling into a political trap that Mr. Netanyahu tried to set for him.

Mr. Gantz’s political stagecraft was put together quickly after the White House extended an invitation to both men last week, while Vice President Mike Pence was visiting Jerusalem. The invitation — the timing of which was seen as Mr. Trump’s latest attempt to distract from the impeachment trial in the Senate — also roiled the political landscape in Israel, where Mr. Netanyahu and Mr. Gantz are locked in a political stalemate.

Mr. Gantz immediately accepted the invitation from the White House. But he reconsidered after seeing Israeli news reports that Mr. Netanyahu was taking credit for inviting him.

The invitation was seen by Mr. Gantz and his advisers as a political trap. Declining to go would hurt him politically in a country where Mr. Trump is viewed overwhelmingly favorably. But accepting would force him to be a bystander as Mr. Netanyahu and Mr. Trump participated in bilateral talks. From Friday morning until late Saturday, Mr. Gantz and his aides debated whether he should attend.

But Mr. Gantz and his team, who have been working for months behind the scenes with Jared Kushner, the president’s son-in-law, and David M. Friedman, the ambassador to Israel, ultimately landed on a face-saving middle ground.

By quietly arranging a one-on-one meeting with Mr. Trump, Mr. Gantz demonstrated out-of-character shrewdness for a man who entered politics only a year ago — and whose appearances without a teleprompter have included enough deer-in-the-headlights interviews that Mr. Netanyahu tried to paint him as “unstable” and more recently mocked him as a stutterer. The meeting also showed how eager the White House is to show off a broad Israeli consensus in favor of its plan.

After aides to Mr. Gantz informed White House officials that they were concerned about the optics of the meeting, Trump officials said they eagerly accommodated Mr. Gantz’s request for a one-on-one meeting with Mr. Trump on Monday.

The meeting was kept quiet until Saturday night and appeared to catch Mr. Netanyahu by surprise. The prime minister then arranged to have his own meeting with Mr. Trump on Monday as well, and he ultimately upstaged Mr. Gantz.

The White House released an official “readout” of Mr. Trump’s meeting with Mr. Netanyahu, calling it a “productive meeting” about the peace plan and bilateral issues, and even briefly allowed the news media into the Oval Office. Mr. Gantz, however, was left to publicize his meeting all on his own.

To top it all off, Mr. Netanyahu was scheduled to have two meetings with Mr. Trump, as well as a joint appearance at the White House on Tuesday when Mr. Trump announces his long-awaited Middle East peace plan.

Instead of a news conference at the White House, Mr. Gantz spoke to the news media — mostly Israeli journalists — in the cramped lobby of The Jefferson before leaving to catch a flight home. In Hebrew, he criticized Mr. Netanyahu, saying no man could run a country and also go to trial.

When he spoke in English, however, Mr. Gantz only praised Mr. Trump, calling the meeting “exceptional” and referring to him as a “true and courageous friend of the state of Israel.”

In fact, the stops that were pulled out for Mr. Gantz were highly unusual for an opposition leader.

Both men met in the White House with Mr. Trump; Mr. Pence; Secretary of State Mike Pompeo; Mr. Kushner; Mr. Friedman; Robert C. O’Brien, the national security adviser; Avi Berkowitz, the Middle East peace envoy; and Brian H. Hook, the special envoy for Iran policy.

“When the president sees an opposition leader, it’s not usually an official meeting,” said Dennis B. Ross, a Middle East peace negotiator under several presidents, including Barack Obama. “An opposition leader will go in and see the national security adviser, and the president will drop in. It’s more informal by definition.”

In the case of Mr. Gantz, “you can’t call him an equal partner, but he’s certainly being treated as a partner,” Mr. Ross said. “It’s clear the administration ceded to his request that he not simply come and look like a prop for Mr. Netanyahu.”

There were certainly some upsides to being in Washington as something of the spoiler. On Monday morning, Israeli journalists spotted Mr. Gantz going for a jog in front of the White House, looking fit and happy in a black windbreaker as he headed back to his hotel.

“It’s a lot harder for the prime minister to go for a jog,” Mr. Ross said. “It suggested he’s taking advantage of his time here. They played it smartly.”

By the time of the big reveal on Tuesday, Mr. Gantz should have returned to Israel and his campaign. He is scheduled to be overseeing a key proceeding regarding Mr. Netanyahu’s attempt to obtain parliamentary immunity from his prosecution on corruption charges.

Annie Karni reported from Washington and David Halbfinger from Jerusalem.