WASHINGTON, June 11 — John Kerry , the presumptive Democratic nominee for president, has repeatedly and personally asked Senator John McCain, the independent-minded Arizona Republican, to consider being his running mate, but Mr. McCain has refused, people who have spoken to both men said Friday.

Mr. Kerry, the Massachusetts senator, made his first direct overtures to Mr. McCain about three weeks after locking up the Democratic nomination in March and approached him again, in person or by telephone, as many as seven times, as recently as last week, according to one person who has discussed the issue with both.

"It was always artfully phrased, but he asked him on several occasions to serve as his running mate," the individual said. "He'd say, `I don't want to formally ask because I don't want to be formally rejected, but having said that, would you do it?' or `I need you to do it,' or `I want you to do it.' "

"It was always phrased in such a way as to give both men plausible deniability," the individual added.

Neither Mr. McCain nor Mr. Kerry could be reached for comment on the rare cross-party running mate discussions. Stephanie Cutter, Mr. Kerry's communications director, said, "Senator Kerry and Senator McCain are good friends and have spoken during the course of the campaign, including when Kerry called McCain to thank him for standing up and defending Kerry against baseless political attacks."

Aides to Mr. McCain did not return repeated phone calls on Friday; his chief of staff, Mark Salter, told the Associated Press, which first reported the discussions, that "Senator McCain categorically states that he has not been offered the vice presidency by anyone."

Less than a month ago, Mr. McCain denied having even casual discussions with Mr. Kerry on the subject.

Word of Mr. Kerry's personal entreaties, and Mr. McCain's flat refusal, may bring an end to the persistent, and at times fevered, speculation among Democrats and others about the potential of a bipartisan ticket, with the two friends and Vietnam veterans matching up against President Bush and Vice President Cheney, neither of whom fought in that war.

Mr. McCain's testy relationship with President Bush, whom he ran against in 2000 for the Republican nomination, fueled the speculation, even though Mr. McCain has repeatedly denied being interested in the job. He said as recently as last week on a late-night television show made clear his lack of enthusiasm about being No. 2, "I spent several years in a North Vietnamese prison camp, in the dark, fed with scraps. Do you think I want to do that all over again as vice president of the United States?"

But his denials did not stop prominent members of Congress - including Senator Bill Nelson of Florida, himself considered a potential Kerry running mate - from suggesting that a Kerry-McCain ticket would be unstoppable in the fall. Mr. McCain showed in 2000 that he could draw Independent voters. A CBS News poll recently found that a Kerry-McCain ticket had a 14-percentage-point edge over Mr. Bush and Mr. Cheney among registered voters, 53 percent to 39 percent, compared to most head-to-head polls that show Mr. Kerry alone tied or slightly ahead of Mr. Bush.

Some Democrats have warned it recent days that the talk about McCain threatened to make whomever Mr. Kerry did select look unexciting by comparison. Among the many potential running mates, those mentioned most frequently include Senator John Edwards of North Carolina, Representative Richard A. Gephardt of Missouri and Gov. Tom Vilsack of Iowa. Indeed, the person who has spoken to both Mr. Kerry and McCain said he believed Mr. Kerry's campaign had deliberately leaked the story on Friday afternoon so it would be lost in coverage of Ronald Reagan's funeral and in the thinly read Saturday newspapers.

A friend of both men said Mr. McCain's rejection of the idea came down simply to his disinterest in being vice president, no matter who is in the White House.

"Kerry and McCain have been close for some time, for years, and there is a comfort level between them," this friend said. "But remember, the first responsibility of a vice president is to be ready to be president, the second is to be comfortable with the president, the third is to know your place. One and two work for McCain, but three doesn't. And I think John McCain knows that he could not be vice president to anyone, whether it be John Kerry or a Republican."

The person who has spoken to both men gave a slightly different reason for Mr. McCain's refusal to consider the job: "At the end of the day, he's a Republican, he supports President Bush's re-election, and while he and John Kerry agree on some major issues, they disagree on more than they agree," the person said. "But the first two of those are more important than the last."

Mr. McCain and Mr. Kerry's relationship began as an acid one; the Arizona senator, a Navy bomber pilot who spent more than five years as a prisoner of war in Hanoi, was outraged by the antiwar activities of Mr. Kerry, a Navy Swift boat commander who famously led protesting veterans in throwing their medals away in 1971.

Mr. McCain campaigned against Mr. Kerry in his first race in 1984, but the two men made peace and worked together during the Clinton administration to resolve the fates of American prisoners of war and service members missing in action, and to normalize American relations with Vietnam.

On the campaign trail until now, Mr. Kerry has cited his friendship and collaborative work with Mr. McCain as evidence of his own ability to reach across the partisan aisle to get things done. He even used Mr. McCain's image in one of his recent campaign commercials, showing a picture of the two senators side-by-side.