Sen. Edward M. Kennedy, (D-Mass.) said yesterday that his mother and his estranged wife have given their approval for a Kennedy presidential campaign next year, thus removing a potential obstacle to such a race. Having said that, Kennedy then went to the White House and lunched with the current occupant, President Carter.

Kennedy's statement concerning the views of his mother and his wife elated his supporters in many states.

Kennedy reiterated to reporters that he is still "not a candidate," but a wide range of Democratic and Republican politicians said yesterday that they thought this new development is a clear signal that Kennedy is edging very close to an active candidacy.

"The assumption here is he's running," said an aide to Sen. Howard H. Baker Jr. (R-Tenn.), a leading Republican presidential hopeful.

"He's running," a prominent Democratic senator said flatly.

But others, including members of the Kennedy camp, cautioned that it would still be difficult for Kennedy to declare a challenge to an incumbent President Carter, assuming that Carter does not withdraw from the race, and that permission from his wife to run did not amount to a solution to Kennedy's potential family problems in a campaign.

Kennedy's White House luncheon invitation was extended earlier in the week, according to a White House official. The two men last met privately early this year.

Asked if the two discussed a possible Kennedy challenge to Carter, the aide chuckled and said: "They discussed SALT, health care, transportation deregulation and other matters of mutual interest."

Word that the Kennedy family had given its blessing to a 1980 presidential run appeared in yesterday's editions of The New York Daily News and The New York Times. The News carried a detailed column by James Wieghart, a journalist long close to Kennedy, reporting without attribution that the family had endorsed a campaign during August, while its members were vacationing together.

The Times attributed its account to "authoritative sources close to" Kennedy who had "let it be known" that the family approved a run.

Reporters yesterday asked Kennedy about these stories, and in response, the senator said, "Both my mother and my wife indicated they would support any decision I would make.

"At this time I am clearly not a candidate," Kennedy said, but then added, "I am very much concerned about the direction the country is going in, and the state of our economy."

News that the Kennedy family would not oppose a 1980 presidential campaign cheered his supporters around the country. Many politicians theorized that this was the purpose of making known the news at this time.

"I'm overjoyed," said Dudley W. Dudley, one of the heads of the key draft-Kennedy organization in New Hampshire. "We could have got along without him," she said, "but there's no doubt it will be a great help, especially on our fund-raising.

Leaders of the draft-Kennedy movements said the signal of his family's attitude was critical to efforts now under way to raise funds across the country to attract Kennedy supporters to the Oct. 13 mass meetings of Democrats in Florida.

At those meetings, delegates will be chosen for a mid-November state convention. A non-binding candidate preference poll at that convention is viewed by supporters of both Kennedy and Carter as the first key test of strength between the two.

A spokesman for the Florida draft-Kennedy group said last night that his group was delighted with the new development regarding Kennedy's family.

There are draft-Kennedy groups in 19 states, and the Federal Election Commission ruled recently that they enjoy a potentially enormous advantage over committees backing declared candidates.

According to the FEC, individual donors can give only $1,000 to a declared candidate, but can give as much as $5,000 cash to as many as five committees seeking the draft of an undeclared candidate, such as Kennedy.

Exploiting this loophole, Kennedy could build a huge war chest, before formally entering the campaign with donations from a relatively small number of contributors.The FEC ruling applies only to the Florida draft-Kennedy group, which sought it, but is expected to be used as the standard for similar draft groups elsewhere.

Authoritative sources yesterday revealed that, beginning in early August, Kennedy's private conversations with political intimates took a new turn, a turn echoed in conversations of the senator's key political aides.

At that time, these sources said, Kennedy began to talk gloomily of the prospects of a devastating Carter defeat in 1980, a defeat that could sweep from Washington the last residue of the legacy left by John F. and Robert F. Kennedy in the 1960s.

Wieghart of The Daily News wrote in his column yesterday that "Kennedy is personally convinced that Carter's political wounds are fatal," the same message he was giving politicians in August. Kennedy is said to point to the national polls that show Carter losing to either Gerald R. Ford or Ronald Reagan in a general election.

Several politicians who heard Kennedy's conversations in August concluded that he had decided to go for the presidency this time, these sources said, though none said so publicly.

Already in July Kennedy had taken an unexpected step that suggested a bolder approach to a potential candidacy. In conjunction with the 10th anniversary of the incident at Chappaquiddick, in which a woman riding in a car Kennedy was driving was drowned, under still-confused circumstances, Kennedy gave long interviews to newspapers and television networks on Chappaquiddick.

In the interviews he said he would have to live with the consequences of that incident, and reiterated his controversial version of what occurred there.

Many politicians saw these interviews as a kind of testing of the waters, to see how Chappaquiddick would play 10 years later. Media and public reaction seemed mild.

Late last month Kennedy made a rare appearance with his wife, Joan, at a New York celebrity tennis tournament in honor of his brother Robert. This provided the occasion for now-unusual photos of Sen. and Mrs. Kennedy smiling together in public.

But friends of Mrs. Kennedy and some of the senator's associates say Joan Kennedy remains a potentially serious obstacle to a presidential campaign, even if she has given it her formal blessing.

Friends say she is still struggling with her publicly admitted alcoholism, and that she has not yet achieved the stability and serenity in her life that she sought by moving out of the Kennedy household in McLean and into an apartment in Boston.

Rose Kennedy, now 87, has long been reported as opposed to a presidential bid by her last living son for fear that he too might be assassinated. According to family friends, she takes a much less active interest in such matters than she once did, and she is now described as willing to see her son run in 1980.

It was hard to find a politician in Washington yesterday who didn't say Kennedy had moved close to an open challenge to Carter. "It looks like this is it," said one of the city's most influential Democrats.