President Carter has given Senator Obama a major boost by calling for the bitter Democratic nomination battle to end on the day of the final primaries on June 3. And he has spoken in glowingly of his ability to “transform the image” of America.

Mr. did not formally endorse Mr. Obama, but in an interview with the Daily Telegraph made clear where his sympathies lie. He even sketched out the kind of inaugural address the first black American president could deliver.

Coming from the most distinguished of some 300 uncommitted super-delegates — the Democratic party leaders who will crown their party’s nominee — Mr. Carter’s comments will be a blow to Senator Clinton’s chances of winning the White House.

“I don’t see any reason at all to continue after June 3 when we know who got the most [pledged] delegates, who got the most popular votes, who won the most states and so forth,” Mr. Carter, 83, said.

June 3 is when the final primaries will be held, in South Dakota and Montana. Mrs. Clinton has a virtually insurmountable deficit among the “pledged” delegates, allocated according to votes, and is highly unlikely to overcome Mr. Obama’s popular-vote lead. But she intends to fight for the nomination all the way to the party’s convention in August.

Her advisers believe her only hope of defeating Mr. Obama would be to persuade the super-delegates that his “electability” against Senator McCain, the Republican nominee, is so questionable that they should put aside the results of the voting and nominate her instead.

Mr. Carter emphasized that he and many other super-delegates would not do this. “It would be undemocratic if the super-delegates blatantly went against the decision of Democratic voters across the nation. And I think that many super-delegates who have not yet declared their preference have the same feeling that I do, including the Speaker of the House Nancy Pelosi. She’s said over and over that whoever gets the most [pledged] delegates by June 3 ought to be the nominee.”

It would be damaging to the party if the battle went to the nomination, he said.

Mr. Carter was himself badly damaged by a long and acrimonious fight for the Democratic nomination in 1980, when he lost in the general election to Ronald Reagan after supporters of Senator Kennedy, his party rival, refused to back him. “It was because of that that the super-delegate premise was pursued and adopted, so now as you know about 20% of delegates will be super-delegates, including me as one of them,” he said.

Mr. Carter, who is promoting a new book, “A Remarkable Mother,” about his mother Lillian, who died 25 years ago age 85, indicated that he felt a close personal bond with Mr. Obama. Both had mothers who worked to overcome racial divisions and who moved abroad in the 1960s to help the disadvantaged ­— Mrs. Carter as a Peace Corps volunteer in India and Mr. Obama’s mother as an anthropologist in Indonesia.

“They were very similar in not being bound by previous custom and willing to break taboos and mores that society establishes that they considered to be inappropriate,” Mr. Carter said.