Updated at 1:19 p.m. ET

A day after the Electoral College made the results official, Senate Majority Leader Mitch McConnell congratulated President-elect Joe Biden and Vice President-elect Kamala Harris for their victory.

McConnell joins a wave of new Republicans acknowledging the win on Monday.

"The Electoral College has spoken. So today I want to congratulate President-elect Joe Biden," McConnell said from the Senate floor Tuesday. "The president-elect is no stranger to the Senate. He's devoted himself to public service for many years."

Biden said he spoke to McConnell after the floor remarks and had "a good conversation."

"I called him to thank him for the congratulations, told him that while we disagree on a lot of things there's things we can work together on," Biden told reporters traveling with him to Georgia. He said he and McConnell agreed to get together soon. "I'm looking forward to working with him," Biden said.

McConnell's comments come more than a month after election results showed the Democratic win. Several moderate members of the GOP had already congratulated the president-elect in those first days and weeks, with more members joining them in recent days.

McConnell also took the opportunity on the floor to recognize Harris' historic win as the next vice president.

"I also want to congratulate the vice president-elect, our colleague from California, Sen. Harris," McConnell said. "Beyond our differences, all Americans can take pride that our nation has a female vice president-elect for the very first time."

McConnell made the remarks at the tail end of a speech on the Senate floor, acknowledging all of President Trump's accomplishments over the last four years — from new judges to progress building a wall along the Mexico-U.S. border to gains for the military.

"The list of American accomplishments since 2016 is nearly endless," McConnell said. "It would take far more than one speech to catalog all the major wins the Trump administration has helped deliver for the American people."

McConnell also closed out his remarks that it was time to end the Trump administration on a positive, bipartisan note.

"I look forward to finishing out the next 36 days strong with President Trump," he said.

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