After the decisive electoral college vote Monday, Senator Mitch McConnell of Kentucky, the majority leader and therefore the most powerful Republican in Congress, finally broke with Trump to congratulate Joe Biden.

“Many of us hoped that the presidential election would yield a different result, but our system of government has processes to determine who will be sworn in on Jan. 20,” Mr. McConnell said in a speech on the Senate floor, after weeks of declining to recognize Mr. Biden’s win. “The Electoral College has spoken. So today, I want to congratulate President-elect Joe Biden.”

He also congratulated Senator Kamala Harris of California, referring to her as the vice president-elect.

“Beyond our differences, all Americans can take pride that our nation has a female vice president-elect for the very first time,” Mr. McConnell said.