Charles and Queen Camilla were greeted by the president and first lady Melania Trump for a morning visit to the presidential mansion while hundreds of guests stood on the South Lawn with the Washington Monument in the distance.
Cannons boomed, temporarily covering much of the scene with smoke, as the US national anthem played.
"What a beautiful British day this is," Trump told the gathering under an overcast April sky to the amusement of the guests from the United Kingdom.
The royal couple are on a four-day state visit to the United States designed to underscore the ties forged between UK and its former colony over the 250 years since American independence, an association known in recent decades as the "special relationship".
In his remarks, Trump referred to the King as "a very elegant man" and joked that his mother "had a crush on Charles".
But he also stressed the bonds of friendship that have evolved between the two countries since their days as adversaries during the War of Independence and the "wounds of war" it caused.
"Think of that very, very long ago difficult war, and yet those wounds did indeed heal into the most cherished of friendships," Trump said.
"The soldiers who once called each other Red Coats and Yankees became the Tommies and the GIs who together saved the free world as brothers in arms and brothers in eternity," the president added in a reference to World War II.
Trump and the King then huddled in the Oval Office for a meeting that was closed to the public, reducing the potential for the freewheeling, sometimes controversial meetings with foreign officials that have become routine during Trump's second term.
Afterward, Trump said it was a "really good meeting" and that the monarch was a "fantastic person".
After the visit to the White House, the King was scheduled to emphasise unity between the US and the UK in a rare address to Congress.
Charles will steer clear of the political acrimony between Trump and UK Prime Minister Keir Starmer but underline their countries' shared values as the duty to promote peace, compassion and democracy while protecting the environment and religious freedom.
The Congress speech is set to last about 20 minutes, a palace source said.
It will focus on the deep bonds between the two countries and how the alliance can benefit global security and prosperity but it will also voice some caution about the US going it alone, and refer to the NATO military alliance and Ukraine.
On Wednesday, the royals will be in New York City to commemorate those killed in the attacks of September 11, 2001 and the trip concludes in Virginia on Thursday with the King meeting people involved in conservation, reflecting his long-standing environmental advocacy.
He will then travel to Bermuda.
with AP
