Although a visit has not been officially confirmed, the King and Queen are expected to make a state visit to the US towards the end of next month, ahead of the 250th anniversary of the US Declaration of Independence in July.
But in a statement, Sir Ed said he wanted the prime minister to advise the monarch that the trip “should be called off”.
“At a time when Trump has launched an illegal war that is devastating the Middle East and pushing up energy bills for British families, it’s clear this visit should not go ahead,” the Lib Dem leader added.
“A state visit from our King would be seen as yet another huge diplomatic coup for President Trump, so it should not be given to someone who repeatedly insults and damages our country.”
Asked about the Lib Dems’ call, cabinet minister Steve Reed said: “I don’t think it is for Ed Davey to decide what the King should or should not be doing.”
Speaking to reporters on Monday, Conservative leader Kemi Badenoch said the trip should not be turned into a “political event”.
She renewed her calls for Sir Keir to authorise the RAF to join “defensive” strikes on Iranian missile sites, accusing the prime minister of being “too slow to protect our bases”.
One Labour MP said the prime minister would “almost certainly” come under more pressure from the party’s MPs to cancel the King’s visit as the date approaches.
They said that MPs facing strong challenges from the Greens at May’s local elections in England were especially concerned about the perception that the government is not tough enough on President Trump.