Facing runoffs, Georgia’s Republican senators ask the state’s top elections official, also a Republican, to step down.

Senators David Perdue and Kelly Loeffler of Georgia on Monday called for the resignation of the state’s top elections official, Secretary of State Brad Raffensperger, as they accused his office of failing to oversee an honest and transparent election without evidence or citing specific concerns.

Their extraordinary joint statement on Monday came as a rift among Republicans in Georgia has intensified as Joseph R. Biden Jr.’s lead over President Trump has steadily grown, pushing the president’s supporters to lash out against Mr. Raffensperger, who is a Republican.

“We believe when there are failures, they need to be called out — even when it’s in your own party,” the senators said in their statement, which did not offer any specific allegations or explain how they believed Mr. Raffensperger had fallen short.

“Honest elections are paramount to the foundation of our democracy,” they said. “The Secretary of State has failed to deliver honest and transparent elections. He has failed the people of Georgia, and he should step down immediately.”

Mr. Raffensperger responded quickly in a statement of his own. “Let me start by saying that is not going to happen,” he said.

“I know emotions are running high,” he added. “Politics are involved in everything right now. If I was Senator Perdue, I’d be irritated I was in a runoff. And both senators and I are all unhappy with the potential outcome for our president.”

Mr. Raffensperger said that the process of reporting results had been orderly and followed the law.

The results in Georgia have drawn widespread notice and alarmed Republicans, as Mr. Biden is outperforming Mr. Trump by more than 10,000 votes in a state Mr. Trump won in 2016. Both senators have been forced into runoff races against Democrats, contests that could determine control of the Senate.

Mr. Trump has continued to falsely insist the election was being stolen from him. The move by the senators, who have both been closely aligned with the president, also underscores the infighting taking place among Republicans even as the party braces for a bitter showdown during the January runoffs.

Some conservatives fear that impugning the electoral process will depress the vote among Republican voters, who may not turn out if they do not trust the legitimacy of the electoral process.

“Trump is gonna cost the GOP the Senate,” Erick Erickson, a Georgia-based conservative commentator, wrote on Twitter. “His supporters are internalizing that the election in Georgia was stolen so why bother even trying.”

In a briefing before the statement was issued on Monday, Gabriel Sterling, the voting system implementation manager for Mr. Raffensperger’s office, sought to debunk the various allegations that had circulated and said the election had run smoothly, despite long lines at times during early voting. He noted that the average wait time to vote on Election Day was two minutes — “that’s unheard of in this state, ever.”

“The facts are the facts, regardless of outcomes,” he said, adding, “In this state, this time, this election on Election Day was an amazing success.”

http://platform.twitter.com/widgets.js