Gov. Charlie Crist of Florida, Gov. Bobby Jindal of Louisiana, and Mitt Romney, the former governor of Massachusetts and a onetime rival for the Republican nomination, have all accepted invitations to visit Mr. McCain at his ranch in Sedona, Republicans said.

After a week of campaigning, Mr. McCain is heading home on Friday for three days without a public schedule. His campaign described this as a social weekend that would include 10 couples, and — as has been its policy — declined to discuss any aspect of the vice-presidential search.

“We don’t talk about the V.P. selection process,” said Steve Schmidt, a senior adviser.

Some of Mr. McCain’s associates said on Wednesday that while these would not be formal interviews, the weekend would provide Mr. McCain a chance to know some of his potential running mates in a social context. He is known as a social and gregarious candidate and senator, and his associates said personal chemistry would be a crucial consideration in his choice.

The identities of the potential running mates who have been summoned to Sedona are not a surprise. And even encouraging the perception that they are under consideration might be more a matter of appearance than political reality: the mere impression that Mr. McCain is considering a running mate from Florida, for example, could help him in a critical state where he campaigned on Wednesday.

Still, the timing — coming as Senator Barack Obama of Illinois appears to have all but nailed down the Democratic nomination — suggested a new focus on a selection process that several Republicans said could prove critical to Mr. McCain’s success in this tough environment. Mr. McCain, arguably more than most presidential candidates in recent elections, has a lot riding on making a choice for running mate that could provide a boost to his candidacy in a tough atmosphere for Republicans.

In addition to Mr. Crist, Mr. Jindal and Mr. Romney, the McCain guest list includes some of his top political counselors, among them Charlie Black, a senior strategist, and Senator Lindsey Graham of South Carolina, his frequent traveling companion and probably his closest colleague in the Senate. Also on hand will be at least one senior business executive prominent in Mr. McCain’s circle, Frederick W. Smith, the chairman of FedEx.

Mr. McCain himself has said his choice of a running mate would draw particular scrutiny from voters given Mr. McCain’s age; he is now 71, or “as old as dirt,” as he likes to joke, while quickly adding that he is in good health. More than that, with Mr. Obama’s selection as his party’s nominee now almost assured, Mr. McCain is contemplating a contest against an energized Democratic electorate after a campaign that has highlighted race and gender issues.

The meeting, which was not disclosed publicly, is taking place on a weekend after Mr. McCain releases his health-care records. The release of those records on Friday is itself a high-profile event that could — by design or not — draw attention away from the gathering.

Mr. McCain said this month that he had assembled a list of about 20 potential running mates. He said he had not decided when he would make a decision; his aides made clear that he would keep the process as closely held as possible.

Among the other potential running mates are Gov. Tim Pawlenty of Minnesota, and Rob Portman, the former director of the Office of Management and Budget who had been an Ohio congressman.

Mr. Crist, a fairly popular first-term governor, has been included on various lists of potential running mates for Mr. McCain, whom he endorsed shortly before Florida’s January primary, which effectively helped Mr. McCain claim the nomination. Mr. Crist said Wednesday that he and Mr. McCain had not discussed the prospect, not even at a fund-raiser in Miami that the two attended Tuesday night.

The McCain campaign, Mr. Crist said, has not solicited the kind of personal information typically requested to vet possible running mates.

As governor of Florida, Mr. Crist, 51, would bring obvious assets to the Republican ticket, beginning with his popularity in a state that is almost always an electoral battleground — and where Mr. Obama appears to be struggling. Mr. Crist’s relative youth could also be an asset for Mr. McCain, who has made clear that age will be a consideration in his search for a running mate.

In Florida, Mr. Crist has long been known for his affability and a campaign skills. Instantly recognizable because of his perpetual tan and striking white hair, Mr. Crist, who was Florida’s attorney general before being elected governor in 2006, has also acquired a reputation as something of a hard-liner on law and order issues.

He supports the death penalty, largely opposes restrictions on the rights of gun owners, early on earned the nickname “Chain Gang Charlie” because he favored allowing convicts to be used in road work, and has described himself as a “pro-life and pro-family” candidate.

Mr. Romney, the former chief executive who ran unsuccessfully for the Republican nomination in 2008 and who was born in Michigan, has made no secret of his desire to join Mr. McCain’s presidential ticket. Mr. Romney’s M.B.A. skills, and business background — including running the 2002 Salt Lake City Olympic Games — could address concerns about Mr. McCain’s ability to manage a struggling economy.

Mr. Romney has also proven himself as a prolific fund-raiser, though he spent enormous sums of money during his campaign and still could not beat Mr. McCain.

Mr. Jindal, who was born in Baton Rouge, La., to a family that had just arrived there from the Punjab area of India, took office in January after serving three years in the House of Representatives. In a race with four candidates, Mr. Jindal, who was born a Hindu but converted to Roman Catholicism as a teenager, won 54 percent of the vote after campaigning as a social conservative, opposing human embryonic stem cell research and abortion in any form, and favoring teaching “intelligent design” in schools as an alternative to evolution.

Julie Bosman, Larry Rohter and Kevin Sack contributed reporting.