Aides to Mrs Clinton, who has made it clear that she would take the job if asked, say that she will make a speech at the Democratic convention in Denver on August 26, and not on the Wednesday night when the vice-presidential nominee is due to appear.

Although Mr Obama still insists that Mrs Clinton would be “on anybody’s shortlist”, the timing of her speech indicates that he is looking elsewhere.

Mrs Clinton, who campaigned for the first time on Mr Obama’s behalf on Thursday, is said to have accepted privately that she will not be on the presidential ticket. A support group pushing for her to be Mr Obama’s running-mate also disbanded on Thursday night.

Her address will come on the 88th anniversary of the ratification of the 19th Amendment, which granted US women the right to vote. It is understood that she will be joined on stage by all her female Senate Democratic colleagues.

Although Mrs Clinton has now agreed to campaign on Mr Obama’s behalf, her husband, Bill, has yet to do so. He has said that he would campaign anywhere that he was asked to appear, but he is still seething over the way he believes his reputation was tarnished during his wife’s campaign – especially over the issue of race, which exploded again this week.

Mr Clinton believes that the Obama camp exploited the issue to damage him and his wife. After John McCain’s campaign on Thursday accused Mr Obama of playing the race card, the top Republican strategists conceded that they had learnt lessons from Mrs Clinton’s campaign and would fight back hard against any perceived effort to accuse them of racism.

The McCain camp accused the Democratic candidate of exploiting the race issue on Thursday after he said that the Republicans were trying to scare voters by telling them that he “doesn’t look like all those other presidents on the dollar bills”.

Rick Davis, Mr McCain’s campaign manager, said: “We’re not going to allow anyone to define John McCain on these terms.” Mr McCain, speaking to reporters in Florida, said Mr Obama’s comments were clearly racial in tone, adding: “I did not bring up the issue.”

One third of Mr McCain’s advertisements are attacks on Mr Obama, a new study shows. The Republican said: “I don’t think the campaign is negative in the slightest.”

Mr Obama, at a separate event in the Florida, denied injecting race into the election. Yet his campaign manager, David Axelrod, conceded that when the Democrat made his dollar-bill remark, part of it was racial.

“He’s not from central casting when it comes to presidents of the United States. He’s young, he’s new to Washington, yes, he’s African-American,” he said.

The row erupted after Mr McCain released an advertisement comparing Mr Obama to Britney Spears and Paris Hilton, an attempt to portray him as somebody more interested in celebrity than the concerns of voters.

Last night the McCain campaign continued the same theme with another advertisement mocking Mr Obama as a narcissistic messiah figure.

Mr Obama said that the McCain camp “seem to be focused on a negative campaign”. An aide described the new advertisement as “downright sad”. Mr McCain said that he was trying to have fun with the videos.

Presidential race

— Barack Obama on the Rev Jeremiah Wright in March: “I can no more disown him than I can my white grandmother ... a woman who once confessed her fear of black men who passed by her on the street.”

— In a radio interview in April Bill Clinton accused Obama's campaign of “playing the race card”. Later, assuming the microphone was off, he said: “I don't think I should take any s**t from anybody on that, do you?"

— Rick Davis, the McCain campaign manager, in a statement yesterday: “Obama has played the race card, and he played it from the bottom of the deck. It's divisive, negative, shameful, and wrong.”