King Charles III flew by helicopter to the H.M.S. Prince of Wales in the English Channel on Tuesday, where he mingled with sailors and watched as fighter jets took off from the deck of the ship, a Royal Navy aircraft carrier. It might have been a welcome getaway from his suddenly complicated social life.

In the span of five days, Charles had invited President Trump for a rare second state visit to Britain and then played host to two of Mr. Trump’s biggest antagonists, President Volodymyr Zelensky of Ukraine and Prime Minister Justin Trudeau of Canada, at his country estate northeast of London.

None of those gestures by Charles was overtly political. As is customary in Britain’s constitutional monarchy, he acted at the behest of the government. But they have nevertheless drawn the 76-year-old king into a swirling diplomatic drama in a way that is almost unheard-of for a British sovereign.

Charles’s invitation to Mr. Trump, delivered with much fanfare by Prime Minister Keir Starmer on Thursday in the Oval Office, has become more contentious since the president clashed with Mr. Zelensky over American support for Ukraine the day after his more harmonious session with Mr. Starmer.

“Now Stop the State Visit for ‘Bully’ Trump,” The Mail on Sunday, a right-wing tabloid, said on its front page. It cited a chorus of demands by lawmakers and other critics that the government rescind the invitation to Mr. Trump to telegraph Britain’s displeasure with the president and solidarity with Ukraine.

Symbolically, Charles may have done the next best thing: hosting Mr. Zelensky at his estate, Sandringham, after the president attended a summit meeting on Sunday devoted to Ukraine. Buckingham Palace did not disclose what they talked about but said Mr. Zelensky was “warmly received” by Charles, who served him tea in Sandringham’s Saloon room.

For Mr. Trump’s critics, the icing on the cake came on Monday, when Mr. Trudeau, whose country has come under sweeping American tariffs and which Mr. Trump says he wants to annex as the 51st state, made the pilgrimage to Sandringham to meet Charles. The king, of course, is also Canada’s ceremonial head of state.

Mr. Trudeau said in a social media post that they discussed “matters of importance to Canadians — including, above all, Canada’s sovereign and independent future.” Charles himself was silent, which frustrated some Canadian politicians, who argued that he should have publicly reaffirmed Canada’s sovereignty. Given his nonpolitical role, that was not going to happen. But the symbolism of the sovereign, smiling as he greeted a prime minister whom Mr. Trump refers to as governor, was lost on no one.

“It’s been a really interesting week in British and royal diplomacy,” said Ed Owens, a royal historian. “People have talked about how this royal family has become a secret weapon for British diplomacy. We saw Keir Starmer wielding the king and the monarchy as such in his interactions with Trump.”

Mr. Owens said Mr. Trump’s well-established affection for the king and the royal family was an intangible factor that could stick in the back of the American president’s mind as he deals with Britain over Ukraine. Mr. Starmer has positioned himself as a bridge between Europe and the United States on the issue. And the president was plainly delighted by the invitation from Charles.

“A beautiful man, a wonderful man,” a beaming Mr. Trump told Mr. Starmer, from the same chair where he sat 24 hours later, as he chastised Mr. Zelensky, telling the Ukrainian president: “Don’t tell us what we’re going to feel. You’re in no position to dictate that.”

Buckingham Palace declined to comment on the status of the invitation to Mr. Trump, noting that the government is in charge of such issues. Mr. Starmer brushed aside calls for the visit to be canceled on Sunday, saying in a BBC interview that critics were “trying to ramp up the rhetoric without really appreciating what is the single most important thing at stake here — we’re talking about peace in Europe.”

Two people with knowledge of the palace said it was highly unlikely that the invitation would be rescinded, given the ill will that would generate with the White House — though the challenge of matching the calendars of two heads of state could mean that the state visit does not take place for months, they added.

In his letter, the king broached the idea of Mr. Trump first seeing him in Scotland, where the president has a golf club, Trump Turnberry, and Charles has a castle, Balmoral, to make the arrangements for the state visit at a later time. The Scotland meeting would be more informal, without the honor guard and lavish banquet in Buckingham Palace that Mr. Trump enjoyed in his last state visit in 2019.

“The idea of it being indefinitely delayed until a peace agreement is reached, on terms that are acceptable to Ukraine and Europe, is interesting,” Mr. Owens said, adding that the royal family “has bought Britain influence within these negotiations that it might not have had otherwise.”

For all his adherence to the monarch’s nonpolitical role, Charles is known to be more politically aware and opinionated than his late mother, Queen Elizabeth II. Early in his reign, he came under criticism for welcoming the president of the European Commission, Ursula von der Leyen, to Windsor Castle, after she signed a deal on Northern Ireland with Rishi Sunak, who was then Britain’s prime minister.

Critics saw it as putting a royal imprimatur on the government’s deal. They said that Charles, whose support of the European Union was well documented, had allowed himself to be used by Downing Street.

The king has been demonstrative in his backing of Ukraine, issuing statements and making regular visits to relief organizations that help refugees from the war. Early in the conflict, when he was still Prince of Wales, he visited a group in London and spoke to a family that had been evacuated from Kharkiv, in eastern Ukraine.

“So, what do you think the aim of the Russians is?” Charles asked them. “Is it to remove people?”

Given the king’s strong feelings and the delicacy of the moment, royal watchers said the government should be careful not to overextend what has so far been a beneficial role. His value as an agent of British “soft power,” they say, resides in his being above politics.

Even his long-planned visit to the aircraft carrier was symbolic, given Britain’s pledge to deploy troops to a peacekeeping force for Ukraine. The H.M.S. Prince of Wales is in training exercises before deploying on an eight-month mission to Asia.

Speaking to crew members in his dress uniform, Charles could have been addressing Mr. Starmer, a relatively new prime minister, who has been struggling to calm the tempest between Ukraine and the United States.

“Your deployment in the next month comes amidst new challenges in an ever-changing and more unpredictable world,” the king said. “It will undoubtedly demand tenacity and determination, both at sea and for those you leave behind at home.”