The maneuver is routine in the Senate to prevent presidents from making recess appointments, which they can do if the Senate is in recess for 10 days or more.

“The current practice of leaving town while conducting phony pro forma sessions is a dereliction of duty the American people can’t afford during this crisis,” Mr. Trump said on Wednesday. “They have been warned.”

If the Senate did not do his bidding, Mr. Trump said, he would use the “very strong power” afforded to him by the Constitution to force an adjournment. He appeared to be referring to Article II of the Constitution, which gives the president the power to adjourn Congress until a time of his choosing if the House and Senate are unable to agree on when they should go out of session.

But there is currently no disagreement between the two chambers — they have already agreed to adjourn on Jan. 3, 2021 — and the office of Mr. McConnell, Republican of Kentucky and the majority leader, suggested in a statement on Wednesday evening that he was not inclined to change that.

A spokesman said that Mr. McConnell had spoken with the president earlier in the day about Senate Democrats’ “unprecedented obstruction” of his nominees and that he shared Mr. Trump’s “frustration with the process.”