President Carter's political advisers are planning to stage a show of force for Carter in the next few weeks in hope of counteracting the enthusiasm that is apparently building around the prospect of a campaign for the presidency by Sen. Edward M. Kennedy (D-Mass.).

The decision to invite some 200 or more "Democratic heavies" from around the country to a pro-Carter gathering here next month emerged from a meeting of about 20 supporters of the president Monday night at the Watergate apartement of Robert S. Strauss, the administration's special ambassador for the Middle East negotiations.

Robert J. Keefe, a political consultant who is working with the Carter-Mondale campaign committee, will coordinate planning of the as yet unspecified pro-Carter event, which will be designed to demonstrate a broad base of support for the president among Democratic elected and party officials.

Such a meeting, participants at the strategy session in Strauss' apartment said, would also send a clear message to Kennedy, who has promised a decision on whether to Challenge Carter in 1980 by the end of the year.

"Sen. Kennedy needs to know what he's up against," said Rep. Bill Alexander (D-Ark.), one of those who attended the Monday night dinner meeting.

Keefe said yesterday the president's advisers have decided it is time to expand the network of Democratic officials already publicly committed to Carter's renomination and reelection. Some of those, such as Detroit Mayor Coleman Young, New York Lt. Gov. Mario Cuomo and Georgia Gov. George Busbee, attended the Monday night session. But Keefe said there are large numbers of other Carter supporters waiting to be mobilized for a public role in the campaign, particularly among Democratic governors and mayors who have worked with the White house for the last 2 1?2 years.

"These people have dealt with the administration and think Jimmy Carter has been a hell of a good president," he said.

Participants at the Monday meeting insisted it was not an "anti-Kennedy" gathering. The plans and intentions of the Massachusetts senators were much on the minds of the Carter advisers, however, as they discussed their political strategy for the coming weeks.

Kennedy's recent statements that he is considering a run for the presidency have dominated political news coverage for the last two weeks and given a clear boost to various "draft Kennedy" organizations around the country. Meanwhile, Carter has remained an unannounced candidate for reelection, a fact that some of his advisers complain is handicapping their efforts at organization and gaining the support of just the kind of Democrats Keefe hopes to bring to Washington next month.

Participants at Monday's meeting, said, however, that advocates of an early reelection announcement by the president received little encouragement from White House chief of staff Hamilton Jordan and press secretary Jody Powell, both of whom attended the session.

Instead, the Carter strategists settled upon the effort to expand the network of the president's supporters, inviting a number of Democratic officials to step forward publicly by attending the gathering planned for next month. Even without an announcement from the president, this could draw a number of key Democrats into the Carter camp early. This would prevent them from delaying their commitments while they assessed the president's chances of withstanding a Kennedy challenge.

Powell told reporters yesterday, "I can't imagine there is any doubt in anyone's mind" that Carter would seek reelection.

In other developments yesterday, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), said he is now convinced Kennedy is seriously considering a challenge to the president. Earlier this week, O'Neill had predicted Kennedy would not run.

In another apparent turnabout, Democratic National Committee Chairman John White said yesterday that a Kennedy-Carter contest would not necessarily split the party, as many have predicted. "It doesn't have to," White said.