The mayor’s return to New York City from overseas was plagued by mishap. The chair of his “reception committee” was late; his aides violated the health code by boarding the mayor’s ship, the Vulcania, before the ship could be screened for contagion.

And reporters — barred from asking questions on political or administrative matters — had the nerve to question the length of the mayor’s journey, which, in an apparent first for a New York City mayor, included a three-day visit to the new nation of Israel.

In the 72 years since Mayor Vincent R. Impellitteri’s voyage in 1951, every single New York City mayor would follow his lead, in recognition of a faith-based political reality: New York City is home to the largest population of Jews outside of Israel.

Mayor Eric Adams upheld that rite of passage this week, visiting Jerusalem and Tel Aviv in a three-day tour highlighted by meetings with Israel’s prime minister, Benjamin Netanyahu, and its president, Isaac Herzog.

The timing of Mr. Adams’s trip seemed potentially fraught, with a crisis now roiling Israeli society over Mr. Netanyahu’s efforts to weaken the independent judiciary. The mayor, however, seemed determined to avoid controversy, and uncharacteristically declined to comment substantively on the debate.

He familiarized himself with Israeli drone technology; lunched on foods like vegan prosciutto and lychee tartare; visited historical sites like the Western Wall and the monument to Yitzhak Rabin, the assassinated prime minister; and toured the national police academy.

“I think we have our own issues,” Mr. Adams said in an interview in Tel Aviv on Wednesday, his last day in Israel. “We have a presidential race coming up. I think we need to be focused on that presidential race. We have a ton of issues.”

Mr. Adams has his own set of challenges, most notably an influx of migrants that he routinely characterizes as among the worst humanitarian crises in New York City history. In a Siena College poll released this week, New York voters disapproved of the mayor’s handling of the issue, 47 percent to 31 percent.

But Mr. Adams contended that his trip to the Middle East was of justifiable importance to the city, saying that he wanted to learn about Israeli technology and efforts to combat antisemitism.

The mayor’s large entourage to Israel this week included several ultra-Orthodox leaders: Chanina Sperlin, a Hasidic leader in Crown Heights, Brooklyn, and a longtime ally who stood with Mr. Adams onstage on election night; Yoel Lefkowitz, a Hasidic leader and New York political operative; and David G. Greenfield, the Orthodox leader of Met Council, a Jewish nonprofit in New York.

Mr. Sperlin and Mr. Greenfield serve on the mayor’s Jewish Advisory Council, created by Mr. Adams as a conduit between his administration and New York Jews; it is dominated by Orthodox men.

Mr. Greenfield contended that the mayor’s itinerary was not focused on Orthodox interests and that the trip would appeal to the broader Jewish community.

“We’re sitting here on the beach of Tel Aviv — that is certainly not an ultra-Orthodox activity,” Mr. Greenfield said.

Still, the political benefits seemed clear.

Voters with distinctive Jewish last names represent 12 percent of New York City’s 4.4 million active registered voters, according to Jerry Skurnik, a senior consultant for Engage Voters U.S., a political consultancy. Of those voters, 62 percent are Democrats and 16 percent Republicans.

In the 2021 citywide election, they represented 16 percent of turnout, although Mr. Skurnik said the actual percentage is likely to be higher because “many Jews do not have distinctive Jewish surnames.”

In the Orthodox and relatively conservative strongholds of Brooklyn, Mr. Adams, the former Brooklyn borough president, has cultivated particularly strong ties.

In the heavily Hasidic precincts of Williamsburg, Crown Heights and Borough Park, Mr. Adams won more than 75 percent of final-round votes in the 2021 Democratic primary, according to John Mollenkopf, the director of the Center for Urban Research at CUNY.

And while there has been generational drift, with younger Jewish voters identifying less strongly with Israel, its appeal to Jewish voters remains strong.

“There’s no question that Jewish voters in New York City want to see their leaders go to the country that they hold so dear,” said David Lobl, a Jewish consultant who helped arrange trips to Israel for former Gov. Andrew Cuomo.

New York City “is the other Jewish homeland outside of Israel and the wellspring of Jewish culture globally in many ways,” said Bill de Blasio, the former mayor, who traveled to Israel three times during his years in elective office.

“Everyone loves their homeland, don’t get me wrong,” Mr. de Blasio added. “But I think the translation of that love and connection, it’s nowhere more palpable than it is for a lot of members of the Jewish community for Israel.”

Israel has been mired in conflict since its founding, and for mayors, traveling there comes with risks and rewards.

When Edward I. Koch traveled to Jerusalem in 1980, part of a 16-day tour of Egypt and Israel, American tourists serenaded him with “I Love New York.”

When Rudolph W. Giuliani traveled to Jerusalem in 1996, he got into an argument with a Long Island family whose Palestinian relative had died in a bus bombing there.

When Mr. de Blasio traveled to the country in 2015, he had to scrap a trip to the West Bank to meet with Palestinians because of security concerns. He met with Israeli-Arab and Jewish schoolchildren instead.

Besides Mr. Adams’s meeting with Mr. Netanyahu, an event that he said made him “proud,” he also met with leaders protesting Mr. Netanyahu’s weakening of the judiciary, which they fear will undermine Israeli democracy.

Both gatherings were closed to the press. Fabien Levy, a deputy mayor for communications who served as his spokesman on the trip, said Mr. Adams also “met with Islamic leaders and community members, including members of the Palestinian community. One even spoke publicly at the dinner we attended last night.”

Mr. Levy declined to provide their names.

Those meetings did little to assuage the concerns of some Muslim New Yorkers, a New York constituency of nearly 800,000 that Mr. Adams has taken pains to cultivate.

“Mayor Adams professes to stand firmly for racial and religious equality, but his trip to an apartheid state contradicts his rhetoric,” said Afaf Nasher, executive director of the Council on American-Islamic Relations of New York.

Mr. Adams said in a brief interview in Tel Aviv that he had relied “for the most part” on Eric Goldstein, chief executive of the UJA-Federation of New York, a mainstream Jewish group that sponsored the trip, to create his itinerary.

“I told them what I wanted to do,” he said, naming priorities like technology and law enforcement.

One of his first stops in Israel was the hospital bedside of a popular Hasidic rabbi. A picture of the visit was posted on X, formerly known as Twitter, with Mr. Adams writing that the rabbi’s “faith and wisdom are unstoppable.”

But Mr. Adams sparked controversy by appearing with Yisrael Gantz, a leader of the settlement movement, who then told reporters that Mr. Adams had agreed to tour the settlements the next time they met. Mr. Adams denied that version of events: “In the entire meeting, the word ‘settlement’ did not come up,” Mr. Adams said on Wednesday.

Mr. Adams made no attempt to visit the Palestinian territories.

“That was not on our agenda at all,” the mayor said.

No mayoral visit to Israel, or trip abroad, comes free of criticism, not even in 1951.

When Mr. Impellitteri returned to New York City, he responded to disapproval of his lengthy absence in what a reporter described as a “tart tone.”

“Up to the time I got on board this ship, I had been working 14, 16 and 18 hours a day, from 8 in the morning until midnight, or 1 o’clock the next morning,” Mr. Impellitteri responded, sounding as aggrieved as a certain modern-day mayor. “My only rest has been on this ship in the last 10 days.”

Patrick Kingsley contributed reporting from Jerusalem.