President Carter laid claim to the Democratic presidential nomination last night and offered "the hand of friendship and cooperation" to his party rival, Sen. Edward M. Kennedy (D-Mass.).

Appearing at a rally of several hundred of his campaign workers and White House aides, Carter said he presumed that Ronald Reagan will be the Republican nominee and said he looked forward to meeting him "both on the campaign trail and in intense, head-to-head debate, to let the American people choose."

"I have not doubt," he added, "that together you and I and all Democrats will triumph in November and return a Democrat to the White House."

The president's brief speech to his supporters -- gathered in a plaza outside a downtown bar, The Buck Stops Here, where they were throwing an end-of-the-primaries party -- was a claim of victory over Kennedy and a call for party unity in the fall campaign. He told reporters on the brief walk to the rally site that he might call Kennedy as early as last night.

Asked what he would say, Carter replied, "I'd congratulate him on running a great campaign."

The losses the president suffered in yesterday's final round of primaries did not appear to faze his aides, who estimated that he would end up with about 2,000 convention delegates, comfortably more than the 1,666 necessary to win the nomination.

"We won where we had to," said Tom Donilon, the Carter campaign's chief delegate counter.

Thus, the tone for the night's celebration was conciliatory. But there remained a certain defensiveness in Carter's remarks about the conduct of the campaign, and his feeling of vindication in a battle with an opponent once thought to be invincible came through clearly.

The president, with his wife, Rosalynn, at his side, began by thanking his supporters for "turning what eight months ago was a prediction of absolute defeat into a wondrous victory tonight."

Carter also thanked his supporters for campaigning in his place so that he could tend to his duties as president -- a reference to his use of the White House as his chief campaign vehicle until Kennedy was all but eliminated, and his refusal to debate his opponent once he gained the advantage over him.

And while declaring his readiness to debate Reagan, the president made no mention of independent presidential candidate John B. Anderson, whom he has said he will not debate in the fall.

Party unity, however, was Carter's main theme as he paid tribute in his speech to Kennedy and his other, long vanquished opponent, California Gov. Edmund G. (Jerry) Brown Jr., neither of whom he mentioned by name.

"I'm now dedicated to bringing out Democratic Party back together, after we have faced two formidable opponents who ran tremendous campaigns, and to reach out a hand of friendship and cooperation to them and their supporters, to share the values and commitments, share the principles, share the future of the Democratic Party and what it stands for," he said.

Declaring that he will be "a very active campaigner in the fall," the president added:

"It's good in a democratic system to have the American people participate, and 15 million Democrats have participated so far in this primary season. Now it's time for the American people to clearly define the issues and to make a choice for the future."

Carter spent several minutes shaking hands with his campaign workers during his 20-minute appearance at the rally, before walking back to the White House.