President Carter was warned today by Sen. Edward M. Kennedy that the domestic budget cuts he is considering for next year could divide the Democratic Party as badly as did the Vietnam War.

Delegates to the party's midterm conference cheered the Massachusetts senator's ringing call for a renewed commitment to traditional Democratic welfare programs and creation of national health insurance.

But they clearly failed to dissuade Carter from his decision to give top priority to military spending in a year of budget austerity.

At two workshops this morning, the president was repeatedly pressed to explain how his administration would justify spending additional billions for weapons while imposing cuts on domestic programs.

At both, the president's answer was the same. "I do not have any apology to make at all for maintaining a strong defense," he told a questioner who had linked military spending to rising inflation. "As long as I am in the White House, I will keep a strong defense."

Five hours after Carter flew back to Washington, Kennedy added his powerful voice to the growing "guns versus butter" debate in a wildly cheered speech that immediately revived talk of a possible 1980 confrontation between the two men for the Democratic presidential nomination.

"The party that tore itself apart over Vietnam in the 1960s cannot afford to tear itself apart today over budget cuts in basic social programs," Kennedy declared.

"There could be few more divisive issues for America and for our party than a Democratic policy of drastic slashes in the federal budget at the expense of the elderly, the poor, the black, the sick, the cities and the unemployed.

"We cannot accept a policy that cuts spending to the bone in areas like jobs and health, but allows billions of dollars in wasteful spending for tax subsidies to continue and adds even greater fat and waste through inflationary spending for defense."

Carter was back at the White House before Kennedy unleashed his warning, but earlier in the day, when Kennedy's friend, Sen. John Culver of Iowa, asserted that defense spending is "relatively speaking the most inflationary dollar you can spend," Carter's response was tinged with annoyance.

Culver was wrong to suggest that it is a waste to build weapons that are never used, the president said, because deterrence is the objective of a strong U.S. military force.

"We build weapons for peace and to let the world know that our nation is strong," he said.

While the Kennedy-Carter difference was clear, there was no direct confrontation at the health policy panel where Kennedy appeared with Stuart Eizenstat, the presidential assistant on domestic policy, and Health Education and Welfare Secretary Joseph A. Califano Jr.

Both administration spokesmen said Carter's step-by-step approach to national health insurance was likely to yield greater progress in the end than early enactment of a comprehensive bill favored by Kennedy.

But neither was directly critical of the senator, and Kennedy, for his part, omitted a paragraph of his prepared speech calling for fulfillment of the platform pledge of national health insurance 'now."

Later, it was announced that Carter aides had agreed that a Kennedy-supported national health insurance resolution would go to the floor Sunday with the president's support. The resolution, approved by a rule-setting committee tonight, urges passage of a health insurance bill in the 96th Congress but is not specific.

The budget emerged as the main point of debate in today's 9-hour round of issues panels, and is expected to provide the focus for Sunday's session, where delegates will finally vote on policy resolutions. For example:

In a panel on the cities, Detroit Mayor Coleman Young -- an early Carter ally -- said it "would be unconscionable to raise defense funds and put the burden on the back of the poor," and put was prolonged applause from the overflow crowd when New York City Council President Carol Bellamy said the conference should find a way to express "our anger" at the president's even considering such a course.

In a panel on foreign policy, national security adviser Zbigniew Brzezinski, challenged by advocates of both bigger and lower defense budgets, said "no vulgar choice between guns and butter is required," but conceded that "you cannot stress too heavily the difficulty of reconciling our social obligations and our defense responsibilities."

In a panel on employment, Ricardo Zazveta, director of a Hispanic jobs program, urged the administration to resist cutting employment efforts. "There is a feeling of negativism here, an unhealthy feeling that we've done too much for minorities," he said. "We've been cut and cut for a long, long time. We've been ignored too long."

Such comments were heard in 24 workshops, supposedly set up to create a dialogue between the Carter administration and the party. There was loud and angry protest against administration policies in every workshop. But it was a formless, scattershot criticism, held firmly in check by administration forces.

"They've over-reacted to us," said Ruth Jordan of Washington. "This is overkill. We went at them with a peagun and they rolled out the cannons."

Carter came to Memphis expecting to encounter criticism from the liberal wing of his party but confident that he would be spared amjor political embarrassment. His most obvious strength, as one White House aide noted before the conference began, is that he is "the only president that the Democratic Party has right now."

But the dissent that surfaced here was a likely foretaste of the resistance that the president's budget austerity policies will confront next year in Congress. And it could signal longer-term political problems for him should serious opposition emerge in the party by reelection year, 1980

For the moment, however, Carter left no doubt that he intends to pursue his defense, budget and anti-inflation policies. And despite the criticism, his aggressive defense of those policies provoked enthusiastic applause at the two workshops he attended.

Before he left Mephis, the president laid a white carnation wreath at the door of the second floor room in the Lorraine Motel where civil rights leader Martin Luther King Jr. was killed on April 4, 1968.

Most of the more than 200 White House and administration officials remained to continued their defense of his policies.

At a panel on cities, nervous mayors had a swarm of questions about rumored cuts in urban aid for presidential assistant Jack H. Watson Jr., Housing and Urban Development Secretary Patricia Roberts Harris and Transportation Secretary Brock Adams.

Watson conceded that there will be "reduced spending" for the Comprehensive Education and Training Act (CETA), the major public service jobs provider, but said final decisions on other urban programs were still at least two weeks away.

Portland Mayor Neil Goldschmidt siad city officials had been told at White House briefings that subsidized housing would be slashed from $38 billion in the current year to $23.5 billion in fiscal 1980. Partnership between the cities and Washington "cannot survive when the federal budget is put on a rollercoaster," he warned.

Detroit's Mayor Young said Newark had been forced to lay off policemen when Congress killed counter-cyclical aid this year, and said the mini-convention must make it clear that "the Democratic Party believes the survival of cities is vital to the survival of the nation."

While most of today's criticism centered on the reports of increased defense spending at the expense of domestic programs, there was some fire from the other flank of the party.

Rep. James Jones (Okla.) told security adviser Brezezinski that "in the face of the tremendous buildup by the Soviet Union" he wondered whether "3 percent real growth in our defense budget is adequate to maintain parity in the mid-80s."

Johnson administration aide Ben Wattenbert told the same panel "there was a great deal of fudging" inside the Carter administration on whether the 3 percent increase would actually be in the budget.