Suspicion that Sen. Edward M. Kennedy is continuing his futile run for president only to ensure President Carter's defeat against Ronald Reagan has been hardened into fact at the White House by pointed remarks attributed to a respected Kennedy lieutenant.

The acknowledged desire to see Carter lose was linked to Washington lawyer-lobbyist James O'Hara, a senior tactician in Kennedy's upcoming floor fight at Madison Square Garden. An account of his remarks was conveyed to presidential aides within hours. O'Hara has unequivocally denied it all, but the source is unimpeachable and totally believed by the White House.

The conversation in question concerned the overriding political puzzle in Washington today: since he cannot be nominated himself and has only the most remote chance of stopping Carter, what makes Teddy run? That question is asked not only by Carterites but by many Kennedy backers. In this instance, it was asked of O'Hara by a pro-Carter Democrat. O'Hara, a former Michigan congressman with close ties to the United Auto Workers, now paractices law in Washington. Chairman of the party's rules commission in 1972 and one of the leading authorities on national convention rules, he will lead the Kennedy floor fight against proposed Rule 11(h) binding pledged delegates to vote for Carter.

The Rule 11(h) fight was raised by the Carter backer in questioning O'Hara. It was becoming the common perception, he said, that this persistent Kennedy effort was aimed at so weakening Carter that he would lose to Reagan in November. That would leave a clear field for Kennedy in 1984, when the political climate might be more in his favor.

According to the account given the White House, O'Hara replied that this perception was "on target." Kennedy considered Carter "unworthy" to be president, said O'Hara, adding that "I think I feel the same way about it." pWhen we asked O'Hara whether he had said this or anything like it, he replied: "Hell, no. That's an outrageous goddamn lie. I'm going to be supporting the nominee of the convention. That's an attempt to discredit me in the rules fight."

But president aides know whom they believe, and it is not O'Hara. In fact, some Carter advisers told us they are furious that O'Hara, whose law firm's clients include the Chrysler Corp., lobbied the Carter administration to bail out the auto company and now is trying to bankrupt the president.

Actually, hopes for Carter's demise go far beyond Jim O'Hara, and their expression is not limited to reports of the O'Hara conversation. On the very night of his disputed conversation, two Kennedy staffers working on the platform were overheard saying much the same thing in the Mayflower Hotel cocktail lounge. One of Kennedy's most important New York backers has told us privately that he and his associates hope the senator will stay in the race to ensure the president's defeat. Another Kennedy backer, who has close connections to the senator's inner circle, told us he is convinced that Kennedy's advisers view 1984 as easier for Teddy if Reagan is elected in 1980. A reagan victory would also help dispose of Vice President Walter F. Mondale, who is not beloved of Kennedy and his closest associates.

This tends to lift the veil of mystery covering Kennedy's political activities since the last round of primary elections June 3. He attended none of the last state conventions picking delegates, has divulged no workable strategy for winning the nomination and has failed adequately to explain his movtives for staying in.

The few Democrats in Congress who endorsed Kennedy for president now look for an end of fighting and a start on reconciliation. In telephone calls to the senator seeking explanations of his present conduct and future intentions, they have been getting Kennedy double talk.

But those congressmen have had better luck than Carter's campaign chairman, Robert S. Strauss. Strauss has gone days on end trying unsuccessfully to reach Kennedy and Steve Smith, Kennedy's brother-in-law and campaign manager, on the telephone. That only confirms the Carter camp's belief in the account of O'Hara's indiscretion. The president's men are now in a mood to counterattack, heightening the prospect for a hot August in New York.