President Carter and Sen. Edward M. Kennedy met for about an hour at the White House yesterday, and Kennedy emerged declaring "I am a candidate for the nomination, and I'm going to continue to seek the nomination . . . I'm planning to be the nominee."

Kennedy said after the meeting that he told the president what he had been saying on the campaign trail for weeks: that Carter owes it to the party to meet Kennedy in open debate. But Kennedy said the prospects that Carter would agree "appear unlikely."

A smiling, zestful Kennedy told a swarm of reporters on the White House lawn that he has "every intention of continuing in this campaign." When a reporter questioned whether he has a prayer of winning the nomination, Kennedy chuckled and said, "More than a prayer."

Although Kennedy won five of the eight Democratic primaries held Tuesday, the end of the primary season has left Carter with about 300 more delegates than he needs to win the Democratic nomination on the first ballot at the party's August convention. Kennedy is about 700 delegates behind.

Carter has declared himself the winner, and some of Kennedy's earliest backers have also said the race for the nomination appears to be over. But everyone agrees that Kennedy will have enough delegates to raise a ruckus at the convention if he chooses to carry his challenge to Carter's more conservative policies that far.

Accordingly, the Carter people have started talking about concilatory steps that might unify Kennedy's liberals with Carter's segment of the party.

One such step was announced yesterday when the Democratic National Committee announced that a prominent liberal, Rep. Morris Udall (D-Ariz.), one of the first members of Congress to endorse Kennedy's presidential bid, will be the keynote speaker at the convention. Udall's office said Carter personally extended the invitation to give the convention's first major speech.

Kennedy had no comment on the choice of Udall, and he declined to answer any questions about whether he and Carter agreed to work for a unified party after the convention.

A few minutes after Kennedy left the White House grounds, reporters were invited into the Oval Office to hear Carter explain his rejection of Kennedy's latest debate proposal.

The president said that the major disagreement between the two is that Kennedy wants "some sort of debate, presumably on television" to work out their differences on economic policy, adding that "I pointed out the best way to do this is through the platform process" at the Democratic National Convention.

Carter also said he promised Kennedy that he and his supporters will "bend over backwards" to treat Kennedy fairly at the convention and in the platform debates.

Kennedy, though, continued to insist that "the best way to [unify the party] would be in a frank and open exchange, a debate" in which the two men could discuss on national television the president's policies on the economy, energy, and foreign affairs, and Kennedy's criticism of them.

A source close to Kennedy said last night that Kennedy told Carter that discussion of the issues by the party platform committee was not an adequate substitute for a debate between the two men.

In some ways, the White House session -- the two contenders' first meeting since the dedication of the John F. Kennedy Memorial Library in Boston last October -- resembled a Kennedy campaign stop.

The challenger arrived on time at 4:30 in the afternoon in a Secret Service motorcade with an entourage that included an advance man, two speech-writers, three press secretaries, a personal aide, a sound man (to send tapes of Kennedy's remarks to radio stations around the country) a nurse, and the traveling press corps. As he drove through the White House gate on Pennsylvania Avenue, a crowd waiting there shouted "Don't quit, Ted."

Afterward, he came out of the West Wing with a broad smile on his face to talk to the 200 reporters and photographers who were waiting in the sun on the White House lawn.

"I finally got to see the Rose Garden," Kennedy said, laughing "Through a window."

As he has done scores of times in the last few weeks, Kennedy fended off all the reporters' suggestions that his cause is hopeless. He responded to most of the questions about his future by repeating his criticism of Carter's economic policies, which he says are harmful to the poor, the unemployed, and the elderly whom Democrats have traditionally represented.

The only point on which the two men apparently agreed was that "lines of communication" should be kept open, with Richard Moe, an aide to Vice President Mondale, and Paul Kirk, Kennedy's chief political adviser, designated chief communicators.

Kennedy had barely finished his news conference before the television Cameras on the White House driveway when Carter countered by inviting reporters into the Oval Office.

The ostensible reason was to witness the president's veto of Congress' repeal of the oil import fee, but when that was quickly completed, the first question concerned the meeting with Kennedy.

"What no questions about the oil conservation fee?" Carter said, feigning surprise.

The president then stood up behind his desk and for more than 10 minutes answered questions about the meeting, an unusual display of presidential accessibility that guaranteed him at least equal time with Kennedy on evening television newscasts.

Carter appeared relaxed, almost serene, as he discussed the meeting, saying it was Kennedy's decision to remain in the race or not, that he had not asked the senator to withdraw and that he remained confident that "regardless of any conceivable circumstances" he will be renominated in August and reelected in November.

The president said the meeting began with a "very friendly" exchange of compliments on the conduct of the primary campaign.

He conceded that he and Kennedy still have differences of opinion on issued, but he zeroed in on the debate question, protraying this as the only serious obstacle to obtaining unification in the Democratic Party.