“Our institutions are actually built for this,” McConnell said. “We have the system in place to consider concerns, and President Trump is 100 percent within his rights to look into allegations of irregularities and weigh his legal options.”

McConnell carries significant influence among Republicans, and his resistance to acknowledging Biden’s win — and support Trump’s efforts — could further drag out the GOP’s opposition and delay the transition process.

Trump has continued to assert that there were widespread irregularities in several states but has so far provided no evidence. He falsely claimed on Twitter that he won the election, even as Biden on Saturday secured the necessary 270 electoral votes to win the White House, according to numerous media projections. The president has even suggested the election was “stolen” from him, but his campaign has lost several court fights already.

McConnell, who met with Attorney General William Barr Monday afternoon, said there should be “no lectures” from Democrats who “just spent four years refusing to accept the validity of the last election.”

“Notably, the Constitution gives no role in this process to wealthy media corporations,” McConnell said. “The projections and commentary of the press do not get veto power over the legal rights of any citizen, including the president of the United States.”

Senate Republicans said they expect the disputes to be resolved sooner rather than later. One GOP senator, speaking on condition of anonymity to candidly describe the party’s thinking, said “most people recognize where this is headed and that clearly Biden is leading in enough states to win, but let's not rush the process.”

So far, only four Republican senators — Mitt Romney of Utah, Lisa Murkowski of Alaska, Ben Sasse of Nebraska and Susan Collins of Maine — have acknowledged Biden’s victory and referred to him as the president-elect.

But like McConnell, most Senate Republicans have refused to publicly acknowledge that Biden will become the next president, even though they admit that’s going to happen in private. While Biden is already aggressively planning his transition to power, GOP senators are deferring to the Trump campaign’s pending legal challenges to the election results in various battleground states.

“I think he’s got a right, a constitutional right to, if there are legal challenges they want to make, and I think everybody ought to let them play out,” Senate Majority Whip John Thune (R-S.D.) said. “Obviously, we’re going to have a result, not for long.”

Sen. Chuck Grassley (R-Iowa) said Trump should not concede yet.

“We’re going to know who is president on December the 14th,” the Iowa Republican said, referring to the date when Electoral College members will vote. “We just better let everything play out.”

Trump’s longshot lawsuits, which hinge on baseless claims of voter fraud, are highly unlikely to alter the results of the election. But Trump campaign adviser Jason Miller said Monday that conceding “is not even in our vocabulary right now,” as the president has been parroting false claims about the integrity of the election.

Even as Biden’s team is preparing for the transfer of power, a top political appointee in the Trump administration is thus far refusing to officially certify Biden as the president-elect. Such a declaration is necessary in order to kick-start the presidential transition process; specifically, it would unlock resources for Biden’s team, including federal funding and access to the federal agencies that will need staffing.

Republicans largely declined to weigh in on whether the appointee, General Services Administration chief Emily Murphy, should certify Biden as the winner, though Collins went as far as to say that Biden and Vice President-elect Kamala Harris “should be given every opportunity to ensure that they are ready to govern” when they take office on Jan. 20.

And Sen. Marco Rubio (R-Fla.), who stood by the president’s right to pursue legal challenges, suggested that the GSA could kick-start the transition process without stepping on Trump’s message.

“I think they need to have that contingency in place,” Rubio said. “I don’t think it would cause any harm to be helpful to the transition. I don’t think it concedes anything. I don’t think allowing GSA to move forward on some of the transition work in any way prejudices any of the legal claims the president intends to bring.”

Romney encouraged the GSA to begin the transition process, adding that “for the purposes of [a] smooth transition and national security we have a national interest in the transition proceeding as rapidly as can be done.”

Senate Minority Leader Chuck Schumer chastised Senate Republicans on Monday for buttressing the president’s position.

“Joe Biden won this election fair and square,” Schumer said. “Too many, including the Republican leader, have been silent or sympathetic to the president’s fantasies.”

John Bresnahan contributed to this report.