The governors of Georgia and Florida, seizing on a tweet from President Trump, made an audacious move on Tuesday, offering their states’ hosting services for the Republican National Convention, which the party is contractually obligated to hold in Charlotte, N.C.

That contract was signed nearly two years ago, and moving a 50,000-person, multimillion-dollar event less than three months before it happens would be extraordinary.

But Mr. Trump — in contrast to the host committee that is coordinating the event — threatened on Monday to move the convention unless Gov. Roy Cooper of North Carolina provided a “guarantee” that there would be no coronavirus-related restrictions on the size of the event. And Mr. Cooper, a Democrat, refused to do so.

“I will say that it’s OK for political conventions to be political, but pandemic response cannot be,” Mr. Cooper said at a news conference on Tuesday. “We’re talking about something that’s going to happen three months from now, and we don’t know what our situation is going to be.”

Mr. Cooper added that his office had asked the R.N.C. to provide a written proposal for holding the convention safely.

Asked about the proposal request and about the overtures from Georgia and Florida, an R.N.C. spokesman, Steve Guest, said: “The R.N.C. wants to hold a full in-person convention in Charlotte, but we need the governor to provide assurances that it can occur. We will need some answers sooner rather than later, or we will be forced to consider other options.”

At an event in the Rose Garden on Tuesday, Mr. Trump said he wanted an answer within a week.

Seeing an opening, Republican governors elsewhere pounced. Gov. Brian Kemp of Georgia started the bidding Tuesday morning, tweeting at the president that his state “would be honored to safely host the Republican National Convention.”

Gov. Ron DeSantis of Florida said he, too, would be delighted to host — “as best we can in accordance with whatever safety requirements,” a caveat that may not please a president looking for a guaranteed full-scale convention.

“Florida would love to have the R.N.C.,” Mr. DeSantis said at a news conference in Miami. “Heck, I’m a Republican — it would be good for us to have the D.N.C., in terms of the economic impact when you talk about major events like that.”

Mr. Trump is not a party to the contract that the Republican National Committee signed with Charlotte and does not have the authority to unilaterally move the convention, though he can exert pressure. His remarks are also out of sync with the conversations that the host committee is having with Mr. Cooper’s office.

Privately, Republican officials are considering options such as allowing only delegates to attend the convention; they have rejected the idea of a virtual event, which Democrats are considering.

Coronavirus cases are still increasing in North Carolina — the confirmed count is over 24,000, with at least 784 deaths — and there is no way for medical experts to predict whether it will be safe for large groups, much less tens of thousands of people, to gather in August. Currently, the state is limiting indoor gatherings to 10 people.

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Mr. Cooper said Tuesday that the conversations his office was having with the R.N.C., and the contingency planning it was requiring, were the same as those happening with sports teams and other organizations hoping to hold large events in North Carolina.

“We have asked them to present a plan on paper to us laying out the various options that we’ve already discussed orally,” he said. “I hope that we can find some kind of reasonable accommodation, but we’re not going to sacrifice the health and safety of North Carolinians.”

Maggie Haberman and Patricia Mazzei contributed reporting.

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