Gov. Ron DeSantis of Florida gave social media a goofy grimace, suggested that Ukraine and Russia seek a cease-fire and praised the policies of former President Donald J. Trump, the man he would need to beat for the Republican presidential nomination, even as he attacked President Biden’s foreign policy.

Mr. DeSantis’s whirlwind trip abroad this week was meant to elevate his credentials as a statesman and heavyweight, while taking him away from the hurly-burly of a fledgling presidential campaign that he has not officially begun.

But if Mr. DeSantis thought it would give him a reprieve from scrutiny, he was mistaken. His trip, which has taken him to Tokyo, Seoul, Jerusalem and, finally, London, with events there on Friday, has been free of any overt gaffes or obvious embarrassments. But his words have been parsed and compared with those of rivals and previous presidential hopefuls. His facial expressions have been examined. Even the placement of his hands has not escaped the notice of the international news media.

“There are people who will always be critical, but I don’t worry about that,” said Kenneth T. Cuccinelli, a former Trump administration official who now leads Mr. DeSantis’s super PAC. “He’s showing himself to be a guy who can go toe-to-toe around the world.”

Mr. DeSantis’s foreign trip, ostensibly a trade mission with some loftier moments intentionally mixed in, no doubt has come at an awkward political moment. Senior Republicans have continued to move toward Mr. Trump, and the head of the Senate Republicans’ campaign arm, Senator Steve Daines of Montana, recently endorsed him. Mr. DeSantis’s position in Republican primary polls has slipped. Key donors have expressed serious misgivings about the governor’s chances, and the largest employer and taxpayer in his state, Walt Disney, has sued him.

Mr. DeSantis needs coverage from conservative media if he hopes to cut into Mr. Trump’s lead, but it has largely ignored his travels. Newsmax did, however, give prominent billing to Mr. Trump’s mockery of his rival’s “emergency Round the World tour,” which Mr. Trump said was to “see if he can remove the stain from his failing campaign.”

But Mr. DeSantis also got much of what he wanted, including meetings with the prime ministers of Japan, South Korea and Israel; news conferences with an international backdrop; and, on Thursday, an address at a Jerusalem conference for Israel’s 75th anniversary.

In a sense, Mr. DeSantis’s trip is a nod to traditional presidential campaigning, before Mr. Trump threw that script in the trash in 2016. In 2008 after they had their presidential nominations sewn up, Senator John McCain and his Democratic rival, Senator Barack Obama, both visited Israel. At the time tongues wagged over Mr. Obama’s decision to tour the occupied West Bank and Mr. McCain’s decision not to.

“It was certainly designed to demonstrate his readiness to grapple with many of the challenges he would face,” said Dan Shapiro, who put together and managed Mr. Obama’s trip and ultimately became his ambassador to Israel, “particularly for a candidate who had not been on the international stage for a long time and was running against a decades-long foreign policy voice in John McCain.”

Mitt Romney, unsuccessfully seeking the Republican nomination, visited Israel in 2007, touring the Holocaust museum Yad Vashem. He returned in 2012, raising the ire of Palestinian leaders by suggesting that cultural differences explained why the Israelis were so much more economically successful than the Arabs under occupation.

“It’s a box that everyone checks,” said Francis Rooney, a former Republican congressman from Florida who was close with Mr. DeSantis when they served together in the House. “It’s a chance for him to show the world, particularly the U.S. electorate, that he has some things to say on foreign policy.”

For Mr. DeSantis, a pugilistic governor known mainly for domestic fights with corporations, educators and Democrats over social policy, the trip has been a chance to discuss foreign policy, though not without some controversy. In Japan, he criticized Germany for not doing enough to bolster Ukraine’s self-defense, while raising the prospects of a bloody stalemate in Ukraine with echoes of the Battle of Verdun during World War I.

“You don’t want to end up in, like, a Verdun situation, where you just have mass casualties, mass expense, and end up with a stalemate,” he told a Japanese newspaper. “It’s in everybody’s interest to try to get to a place where we can have a cease-fire.”

He praised the U.S.-Japan alliance to which Mr. Trump was at times hostile, and took some voter-pleasing jabs at China.

But the statecraft choreography was left mainly to Thursday’s leg in Israel, which came at a fraught moment. Israel’s new government, the most right-wing in its history, has drawn tens of thousands of protesters to the streets and alienated many American Jews. Mike Caruso, a Republican Florida state representative, said in an interview from Jerusalem that he rushed a bill through the Legislature in Tallahassee this week to increase criminal penalties for antisemitic and other bias crimes so the governor could sign it ceremonially in Jerusalem.

“They love him in Israel, I can tell you that,” Mr. Caruso said. “I’ve never seen a more inviting crowd. When he walked into the room, it just lit up.”

And at a news conference where Mr. DeSantis favored conservative outlets from the United States and Israel, he took a swipe at the Biden administration, criticizing the deterioration under Mr. Biden in relations between the United States and Saudi Arabia, and suggesting that Washington should avoid taking sides in Israel’s domestic debate about the future of its judiciary. Mr. Biden has taken an increasingly vocal stance against efforts by the far-right Israeli government to assert greater control over the country’s Supreme Court.

“We must also in America respect Israel’s right to make its own decisions about its own governance,” Mr. DeSantis said. “You’re a smart country, you figure it out; it shouldn’t be for us to butt into these important issues.”

He also flagged his efforts as governor in targeting Airbnb, after the travel listings company briefly removed from its website properties in the Israeli-occupied West Bank a few years ago. Mr. DeSantis also repeated his long-held position on the West Bank, which the governor says is “disputed” territory and which he referred to as “Judea and Samaria,” the biblical name for the territory used by right-wing Israelis.

His stance is at odds with that held by most countries, which consider the West Bank occupied territory because it was captured by Israel from Jordan during the Arab-Israeli War of 1967.

But in embracing the Israeli far right and its positions on domestic and Middle Eastern affairs, Mr. DeSantis was obliquely praising the policies of the Trump administration. While never mentioning Mr. Trump by name, Mr. DeSantis tried to differentiate himself from his rival by noting that he had pushed the administration to move the U.S. embassy to Jerusalem from Tel Aviv, months before Mr. Trump decided to do so.

Mr. DeSantis also hailed the deals between Israel and the Persian Gulf states brokered by Mr. Trump, known as the Abraham Accords, and said that he supported efforts to secure a new one between Israel and Saudi Arabia.

“It would be petty of the governor to not acknowledge that accomplishment,” Mr. Cuccinelli said, “and he is not petty.”

The governor’s performance in Israel could shore up his standing with conservative evangelical Christians, the most stalwart supporters of the Israeli right, as well as with wavering Republican donors. Miriam Adelson, a Republican megadonor who was part of the proceedings on Thursday in Jerusalem, has been a strong supporter of Mr. Trump, but since the death of her husband, the casino magnate Sheldon Adelson, she has pulled back her giving to Republican candidates.

But in a world where nothing dies on the internet, said David Jolly, a former Republican House member from Florida who left his party in disgust during the Trump era, the most lasting image of Mr. DeSantis’s trip might be the goofy face he made in Tokyo when asked about polls showing him well behind Mr. Trump. His answer — “I’m not a candidate, so we’ll see, if and when that changes” — will be forgotten but his odd expression might not be.

“When confronted on the world stage, you saw him physically react and flail,” Mr. Jolly said. “Those memes are going to live on for a long time.”

Motoko Rich contributed reporting from Tokyo, and Choe Sang-Hun from Seoul.