Sen. Edward M. Kennedy said today that he needs to win the California primary June 3 to carry his challenge to President Carter into the Democratic National Convention.

"I'm planning to win California, and I expect to win," Kennedy said.

He described the primary as "essential" not only to his chances for nomination but also to staying in the race at all after the June 3 round of primaries. The latest United States International count gives Carter 1,562 delegates and Kennedy 832, with 1,666 needed for nomination.

By the estimates of both the Kennedy and Carter camps, the race in California is extremely close. The California Poll of Mervin Field, published today, shows Kennedy and Carter tied at 33 percent apiece, with the other third of the vote undecided or going to other candidates.

Kennedy declined to say whether he expected to win in Ohio and New Jersey, the other populous states among the eight that will hold primaries June 3. A total of 696 delegates to the Democrtic National Convention will be selected, including 306 in California.

Kennedy, in a relaxed mood at a bacon-and-eggs breakfast with reporters, was unusually candid about the problem facing him in his battle against Carter. Asked if he has sufficient funds to make an impact in California's vast media market, Kennedy replied:

"We're very hard-pressed for money to have an effective media buy. We probably should have started two weeks ago. We don't really have the resources we need to raise the level of consciousness in the state."

Nonetheless, Kennedy said he expects to carry California, where he has been concentrating his campaign effort.

After an early-morning speech and the breakfast here, Kennedy flew to Oakland and San Francisco for more campaigning. He is scheduled to return to Los Angles Saturday.

Kennedy sharply criticized Carter, describing the president as having demonstrated "fundamental incompetence" on foreign and domestic policy. The Massachusetts senator acknowledged that he resented Carter's campaign commercials in Ohio, which featured man-in-the-street interviews questioning Kennedy's character and Senate record.

Kennedy said the commercials were "demeaning the office" of the presidency and were a poor substitute for Carter's willingness to debate the issues with his challenger.

Asked if Carter would benefit from rapidly sinking interest rates and a moderation of inflation, Kennedy said these achievements were being accomplished by increased unemployment and that inflation remained double-digit.

"What Carter is saying is that the country is getting better because it's getting sicker at a slower rate," Kennedy said.

Kennedy continued to insist that it will be possible for the Democrats to unify after the national convention. But there are signs among some in his audiences that such unity may be hard to achieve.

At UCLA Thursday night, Kennedy was asked if he would support Carter if the president wins the nomination. Before Kennedy could give his standard answer that the nomination hadn't been decided yet, the students yelled, "No, no."