In prepared remarks to officials from both countries, as well as hundreds of spectators, Mr. Trump largely stuck to a script. He praised the Anglo-American relationship in lofty terms, describing it as having birthed a “revolution in human freedom” that was “never, ever extinguished, but carried forward across centuries, across oceans and across history, until it became a fire that lit the entire world.”

The king’s message to Congress — describing a history of “reconciliation and renewal” between the United States and Britain — is intended to advance his government’s priorities without pulling him into the dispute between Mr. Trump and Prime Minister Keir Starmer over the Iran war.

On Tuesday evening, the king and Queen Camilla will attend a banquet in the White House’s State Dining Room. It follows a similar dinner that the king hosted for Mr. Trump at Windsor Castle in September.

The royal couple will leave Washington on Wednesday for events in New York City, including a morning visit to the Sept. 11 memorial and a celebrity-filled gala in the evening. They will conclude the trip on Thursday with a visit to Arlington National Cemetery and several stops elsewhere in Virginia.

Here’s what else to know:

• Tight security: Days after a gunman breached security in an attack on a gala dinner in Washington attended by Mr. Trump, measures for the state visit include both highly visible and unseen layers of Secret Service protection.

• Visuals only: British officials have been eager to avoid an awkward public moment in which Mr. Trump might belittle Mr. Starmer with the king at his side. As a result, there was only a brief photo opportunity before their meeting on Tuesday, with no chance for reporters to yell questions.

• Returning the favor: At September’s Windsor Castle banquet, Mr. Trump called the invitation “one of the highest honors of my life.” In his toast, the president added that Charles had for decades “epitomized the fortitude, nobility and the spirit of the British monarchy and the British people.”

• Beyond Washington: British officials said the four-day royal trip was planned to allow the king and queen to also spend time outside the nation’s capital. In New York, the king will meet with young people in Harlem, while the queen tours a Winnie the Pooh exhibit at the New York Public Library. In Virginia, the king will attend a “block party” near the Shenandoah mountains, and the queen will visit a farm dedicated to the horse racing industry.

On a state visit designed in part to repair U.S.-British relations, King Charles’s schedule does not include plans to see his younger son, who lives in the United States with his family.

One meeting that appears to be absent from King Charles III’s carefully planned schedule in the United States this week is any reunion with Prince Harry.

On a four-day state visit intended in part to repair bruised U.S.-British relations, Charles’s itinerary currently includes no plans to see Harry, his 41-year-old son, who lives in California with his wife, Meghan, and their two children.

Buckingham Palace officials declined to comment when asked whether the king and his younger son would meet. Charles and Queen Camilla are scheduled to be in Washington on Tuesday and New York on Wednesday before departing on Thursday.

The family fell out publicly when Harry, who holds the title Duke of Sussex, withdrew from royal duties in 2020 and relocated to California in an act of self-exile. In the years since, their relationship has been tested again and again.