Mrs. May hopes that, by the time of Mr. Trump’s visit, Parliament will have approved her plan for Brexit, and Britain will be on course to leave the bloc, perhaps at the end of June. She has said that sometime after that she would step aside for a new leader.

But with no sign that her Brexit plan will be approved soon by Parliament, the state visit could come at a time of significant political tension over Mrs. May’s leadership. Because of the latest delay to Brexit, Britain is likely to hold elections to the European Parliament on May 23. If that contest goes ahead as expected, experts predict that the results are likely to be bad for Mrs. May’s Conservatives, and to fuel discontent within her party.

Until Britain leaves the European Union, it will not be able to start formal negotiations on any new trade agreement with the United States, even if Mr. Trump offers to help facilitate one.

On June 5, the president will take part in events in Portsmouth, on the south coast of England, for the 75th anniversary of the D-Day landings in Normandy, the White House said, adding that the next day, Mr. and Mrs. Trump would travel to France at the invitation of President Emmanuel Macron.

A formal invitation for a state visit, issued by the monarch on the advice of the government, is among the heaviest tools in Britain’s diplomatic arsenal. Before Mr. Trump, Barack Obama and George W. Bush were the only two American presidents who had been invited to Britain for a full state visit.

Mr. Trump mostly avoided London on his last visit, when protesters made it clear that he would not be welcome in the capital.

John Bercow, the speaker of the House of Commons, has said that he will not allow Mr. Trump to address Parliament, as other leaders, including Mr. Obama, President Xi Jinping of China and former President Nelson Mandela of South Africa, have done.