On Sunday, Georgia’s lieutenant governor, Geoff Duncan, and Mr. Raffensperger both said in television interviews that it was clear that Mr. Biden had won the state. But in a debate that evening between Ms. Loeffler and her Democratic rival, the Rev. Raphael Warnock, Ms. Loeffler declined to say, when questioned, that Mr. Trump had lost the election.
Mr. Trump has been pushing Gov. Brian Kemp, a Republican, to order an audit of voters’ signatures on ballots. The governor has said that he would also like to see an audit, but he has argued that his office does not have the authority to order one.
The president had also urged the governor to order a special legislative session in which lawmakers might assign a new slate of Electoral College members who would favor him. But the governor repeatedly declined to call for a special session, and he said in a statement on Sunday that such a gambit was not allowed by state or federal law.
Yet Mr. Trump continued to pound away at Mr. Kemp on Monday. “The Republican Governor of Georgia refuses to do signature verification, which would give us an easy win,” he wrote on Twitter. “What’s wrong with this guy? What is he hiding?”
It was unclear how an audit of signatures might help Mr. Trump’s cause. When absentee ballots are processed by county elections officials, they come in envelopes with the voters’ signatures on the outside. These signatures are checked against the signatures in state databases. But the envelopes are then separated from the ballots to ensure voters’ anonymity. That means that individual ballots could not be questioned even if problems with the signature-matching process were to come to light.
A top official in Mr. Raffensperger’s office, Gabriel Sterling, also spoke at the news conference on Monday and addressed other misunderstandings and unfounded conspiracies, sarcastically referring to the presentation as “Disinformation Monday.”
Among other things, Mr. Sterling denounced as bogus a claim that suitcases of ballots were illegally brought into a Fulton County elections center, and a rumor circulating on the internet that two Democratic state senators had been involved in counting ballots.
Also on Monday, a federal judge in Atlanta tossed out a lawsuit alleging a vast conspiracy to hack into and manipulate voting machines in Georgia. The suit had been filed by Sidney Powell, a former lawyer for Mr. Trump whom his campaign has disavowed.
Richard Fausset reported from Atlanta, and Nick Corasaniti from New York. Alan Feuer contributed reporting from New York.