WASHINGTON — Speaker Nancy Pelosi invited President Trump to give the State of the Union address on Feb. 4, a sign that business is operating as usual in the nation’s capital, even after the House impeached the president two days ago.

In a letter to Mr. Trump on Friday, Ms. Pelosi wrote, “In the spirit of respecting our Constitution, I invite you to deliver your State of the Union address before a joint session of Congress.”

The president accepted the invitation, said a White House spokesman, Hogan Gidley.

While the invitation is customary, it was notable this year because the president has lobbed insults at Ms. Pelosi in recent days for leading the House to approve two articles of impeachment against Mr. Trump related to his pressure campaign on Ukraine.

The last sessions for both the House and the Senate were Thursday, and the president planned to leave town on Friday before the holiday next week. Questions remain about when Ms. Pelosi will send the charges of abuse of power and obstruction of Congress to the Senate to set in motion an election-year trial.