CNN  — 

President-elect Joe Biden urged the country “to lower the temperature” in his victory speech on Saturday night, but Republican leaders he’ll have to work with in Congress have either urged President Donald Trump to not concede or stayed silent despite no widespread evidence of fraud in the election.

Senate Majority Leader Mitch McConnell, who is likely to limit the scope of Biden’s agenda, has not commented since Friday, the day before the race was called, when he called for “every legal” vote to be counted, while House Republican leader Kevin McCarthy echoed Trump’s claims that the election isn’t over yet.

“We’ve had the most competitive presidential race in our modern history,” McCarthy said on Fox News on Sunday. “That’s why every vote should be counted, every recount to go forward, and every challenge should be heard.”

The Republican Party is split over how to handle Biden’s victory, as Trump continues to dispute the result. While a small contingent of conservatives want to restore faith in the democratic process, Trump’s fiercest supporters have adopted the President’s mantra to “fight back very hard” when he feels personally mistreated.

“This is a contested election,” Senate Judiciary Chairman Lindsey Graham said on Fox on Sunday. “The media doesn’t decide who becomes president, if they did, you would never have a Republican president forever.”

“Do not concede, Mr. President, fight hard,” the South Carolina Republican added.

Sen. Roy Blunt of Missouri, a member of GOP leadership, said on ABC’s “This Week” on Sunday that “it seems unlikely that any changes could be big enough to make a difference, but this is a close election.”

“I look forward to the President dealing with this however he needs to deal with it,” he added.

The party’s responses in the aftermath of the election seem to split its past from its future.

Former President George W. Bush and Utah Sen. Mitt Romney, the Republican party’s 2012 presidential nominee and a frequent Trump critic, congratulated Biden and Vice President-elect Kamala Harris. Romney called them “people of good will and admirable character” and said he would “pray that God may bless them in the days and years ahead.” Bush called Biden a “good man, who has won his opportunity to lead and unify our country.”

And Tennessee Sen. Lamar Alexander, a former governor and secretary of education who is retiring after a four-decade career in public office, said on Saturday that the presidential candidates should fulfill their democratic duty and accept the will of the people.

“After counting every valid vote and allowing courts to resolve disputes, it is important to respect and promptly accept the result,” tweeted Alexander. “The orderly transfer or reaffirming of immense power after a presidential election is the most enduring symbol of our democracy.”

But Alexander’s Republican incoming successor in the Senate, Bill Hagerty, Trump’s former ambassador to Japan, said that he had contributed to Trump’s legal fund to protect the “integrity” of the election, and retweeted Trump’s statement that “this election is far from over.”

Biden triumphed in Wisconsin, Michigan and Pennsylvania – three states that 2016 presidential candidate Hillary Clinton lost – on his way to winning the White House, and currently leads Trump in Arizona and Georgia.

Addressing the nation on Saturday before a parking lot in Delaware full of honking supporters, Biden and Harris called on the country to heal after a divisive election.

“It’s time to put away the harsh rhetoric, to lower the temperature, to see each other again, to listen to each other again,” Biden said.

But just hours earlier, Trump again falsely claimed that the election was stolen from him, baselessly alleging that election observers were not present at the polls.

“I WON THE ELECTION, GOT 71,000,000 LEGAL VOTES,” tweeted the president. “BAD THINGS HAPPENED WHICH OUR OBSERVERS WERE NOT ALLOWED TO SEE. NEVER HAPPENED BEFORE. MILLIONS OF MAIL-IN BALLOTS WERE SENT TO PEOPLE WHO NEVER ASKED FOR THEM!”

While some prominent Republicans are defending the President, publicly at least, some of those closest to him have taken a different approach in private. Jared Kushner, Trump’s son-in-law and senior adviser, has approached the President about conceding the election, two sources told CNN Saturday. And first lady Melania Trump has advised the President the time has come for him to accept the election loss, a separate source familiar with the conversations told CNN on Sunday.

The President’s refusal to concede is obscuring what otherwise was a positive showing for the GOP this year. Republicans unexpectedly gained seats in the House and defeated extremely well-funded Senate Democratic candidates in Maine, Iowa, Montana and elsewhere.

“In the Senate, virtually every candidate, even those who were wildly thought to be on the way to winning, over performed,” Billy Piper, a former McConnell chief of staff, told CNN. “That’s a good night.”

“It actually appears that in the middle of absolutely horrible circumstances, America has once again run the election it should be proud of,” he added. “The fact that we are counting 150 million ballots as quick as we are, given the uniqueness of how they had to be cast, it’s pretty amazing.”

The President’s refusal to accept the results could also complicate the GOP’s hopes of holding onto the Senate. Democrats’ chances of winning the chamber have been reduced to flipping both of Georgia’s Senate seats in two likely January runoff elections in a state that hasn’t elected a Democratic senator in 20 years.

Kristin Wilson contributed to this report.