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Top Senate Republicans are officially accepting President-elect Joe Biden's 2020 victory after the Electoral College confirmed his win on Monday.

Their acceptance of the president-elect's victory comes nearly six weeks after the Nov. 3 election, as President Trump refuses to concede while making claims of widespread voter fraud that have so far been unsubstantiated.

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

Sen. John Thune, R-S.D., speaks during a Senate Transportation subcommittee hybrid hearing on transporting ​a coronavirus vaccine on Capitol Hill, Thursday, Dec. 10, 2020, in Washington. (Samuel Corum/The New York Times via AP, Pool)

He went on to congratulate Vice President-elect Kamala Harris, saying that despite political differences, "all Americans can take pride that our nation has a female vice president-elect for the very first time."

"Many millions of us had hoped the presidential election would yield a different result. But our system of government has processes to determine who will be sworn in on January the 20th," McConnell said.

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Before McConnell's speech, which began by praising Trump's accomplishments and "tireless work," Senate Chaplain Barry Black mentioned Monday's Electoral College vote and asks for "blessings" for Biden and Harris.

Other Republicans also jumped on the congratulatory bandwagon on Monday.

"At some point, you have to face the music," Sen. John Thune of South Dakota told the Associated Press Monday. "Once the Electoral College settles the issue today, it’s time for everybody to move on."

Sen. Roy Blunt of Missouri, chairman of the inaugural committee, said the panel will now "deal with Vice President Biden as the president-elect."

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Just last week, the Republicans on the inauguration committee had declined to publicly acknowledge Biden's win over Trump. Blunt said Monday’s Electoral College vote "was significant."

Sen. John Cornyn of Texas said barring further legal challenges, it appears Biden will be president.

Sen. John Cornyn,R-Texas arrives for the continuation of the Senate impeachment trial of President Trump at the U.S. Capitol in Washington. (REUTERS/Erin Scott)

"That’s sort of the nature of these elections. You got to have a winner. You got to have a loser," Cornyn told the AP, adding that once Trump's legal arguments are exhausted, "Joe Biden’s on a path to be president of the United States.”

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Other Republican lawmakers will continue to fight election results until Jan. 6, when Congress will vote on whether or not to accept the Electoral College's results. Some have suggested that the president's legal battle should continue until the inauguration on Jan. 20.

"It’s a very, very narrow path for the president," Sen. Lindsey Graham of South Carolina said. "But having said that, I think we’ll let those legal challenges play out."

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The Associated Press contributed to this report.