And Senator Susan Collins of Maine, who was among the first Republicans to recognize Mr. Biden's victory, said in a statement on Friday that there was "a right way and a wrong way for the incumbent president to pursue his rights to contest what he perceives as election irregularities."
"The wrong way is to attempt to pressure state election officials," she said. "That undermines the public's faith in our election results without evidence and court rulings to support the allegations."
The criticism also came from other Republicans not known for challenging Mr. Trump. Senator Joni Ernst of Iowa, a member of Mr. McConnell's leadership team, on Thursday called some of the election fraud claims "absolutely outrageous," though she did not fault the president.
Ms. Granger, who was re-elected to represent a conservative district based in Fort Worth, was more direct: She told CNN that she had "great concerns" about what Mr. Trump was doing.
"I think that it's time to move on," she said.
But the most scathing criticism came from lawmakers who had no voter backlash to fear. Representative Paul Mitchell of Michigan, who is retiring, wrote in an op-ed in The Detroit News that Mr. Trump's "continued refusal to acknowledge the election results risks corroding our democracy by literally hollowing it out."
"If we no longer believe in our own system -- with our local elected clerks following the laws -- then our ability to choose our leaders is at fundamental risk, as is our system of governing," he wrote in the piece, which was co-signed by Representative Elissa Slotkin, Democrat of Michigan.
Representative Tom Reed, Republican of New York, suggested that many in his party were torn between the facts and the views of their constituents who believe Mr. Trump's assertions that he was defrauded of victory.