President Carter and Sen. Edward M. Kennedy, still unofficial opponents for the Democratic presidential nomination, are seeking to corner the support of prominent party leaders.

The president will jump first in this age-old game of endorsements with a dinner tonight at the Hyatt Regency Hotel that campaign strategists predict will attract about 500 supporters from around he country.

The dinner is free, but it carries a political price tag: Those who attend have been told that their presence will be considered "tantamount to an endorsement" of Carter in his race against Kennedy.

"If anyone there suggests they just came for dinner, they are not being honest with themselves, with you or with us," Robert J. Keefe, a political consultant who arranged the dinner for the Carter reelection committee, said yesterday.

Kennedy, meanwhile, has spent the last several days in an intensive series of talks with his allies on Capitol Hill and in telephone conversations with potential supporters around the country.

Sources said the Massachusetts senator was not seeking public endorsements at this time, but was attempting to solidify and enlarge his network of loyalists in preparation for a public announcement of his candidacy.

Carter is scheduled to announce for reelection on Dec. 4. Kennedy's announcement is widely expected next month.

But since last Saturday's dedication of the John F. Kennedy Presidential Library in Boston -- a solemn occasion attended by both the president and Kennedy -- their unofficial battle for the Democratic nomination has clearly entered a new stage.

Tonight's Carter dinner will provide the latest example of one of the advantages the president carries into that battle -- incumbency.

According to congressional sources, White House congressional liaison officials have been pressing members of Congress for their attendance at the dinner, and with it, their endorsements. Those who accepted will be treated to a reception at the White House before boarding buses for the trip to the hotel.

In planning the dinner, Carter campaign stratregists hoped to use the occasion to increase what they consider their lead in organizational strength over the Kennedy forces. By inviting prominent Democrats to step forward publicly this early, the president's strategists reasoned, they might prevent some defections to Kennedy and would gain public commitments that can be called on in the weeks ahead as the battleground shifts to state caucuses and primary elections.

Keefe said yesterday the effort to identify sources of organizational support has been particularly successful in New York and Texas.

"We had two problems," he said of the thinking that led to the dinner. "It seemed we had substantial support that was not being organized or developed -- beginning at the top. And we have a candidate who has a certain advantage of incumbency that will cause some people to endorse him if they are asked and to duck if they are not asked. Politicians like options, not commitments."

By calling for those commitments now, the Carter campaign may gain the endorsements of some Democrats who, absent a direct request from agents of an incumbent president with all that implies about future favors, would be more than content to remain on the fence for now. But it isn't clear whether this technique will produce significant numbers of new Carter supporters.

The New York delegation to the dinner, for example, will include Mayor Ed Koch, former mayor Abe Beame and Lt. Gov. Mario Cuomo, according to Keefe. All have long been considered in the president's camp.

The same is true of Sen. Lloyd Bentsen, who will head the Texas delegation, and of some others expected to attend, including Connecticut Gov. dElla T. Grasso, Detroit Mayor Coleman Young and New Jersey Gov. Brendan T. Byrne, who on Thursday will benefit from a fund-raising appearance by Carter in East Rutherford, N.J.

One person the Carter camp clearly would like to see show up is Chicago Mayor Jane Byrne, who was assiduously courted by the president in Chicago last week. Keefe said Bryne had been invited but said he did not know whether she would attend.

It was also not clear yesterday whether everyone attending the dinner will consider it an endorsement of Carter. District of Columbia Mayor Marion Barry does not, according to his press secretary, Florence Tate.

Tate said Barry is "supporting President Carter at this point" because "nobody else has announced."

Kennedy's announcement, however, now appears to be only a formality. In the last few days, prominent Democrats from New Mexico to New Jersey have received calls from the senator or his brother-in-law and campaign chief, Stephen E. Smith, assuring them that Kennedy is preparing to run and wants their support.

Some calls have gone to longtime friends of the family, such as New York Gov. Hugh Carey. Elsewhere, the Kennedy strategy appears to be to try to offset prominent Carter support.

In New Mexico, for example, where Gov. Bruce King is considered a strong Carter man, the Kennedy forces are working on Lt. Gov. Roberto Mondragon. To offset Grasso's support of the president in Connecticut, Kennedy has talked to state party chairman John Dempsey Jr., normally a close Grasso ally.