Sen. Edward M. Kennedy (D-Mass.), AFL-CIO President George Meany and other leaders of labor and the elderly broke with President Carter yesterday and accused him of planning to send Congress an inadequate "piecemeal" start on a national health insurance plan.

Kennedy, in a joint news conference with Meany and a broad coalition of pro-health insurance groups, charged Carter with "a failure of leadership on this issue" and misreading the mood of the people.

Kennedy, until now one of Carter's most consistent Senate supporters, bluntly labeled as unacceptable a Carter plan to phase in a comprehensive health insurance plan only if certain economic and other conditions are met.

Kennedy said this would "cripple any program from the start," and disappoint millions whose "voices are seldom heard in our government."

Shortly after Kennedy and the coalition finished, Health, Education and Welfare Secretary Joseph A. Califano Jr. made a hastily announced appearance in the White House press room. He said the president is "deeply committed" to "decent health care for every American," but is convinced that a health plan must be "phased in a rational and cautious manner" that meets "budgetary and economic realities," avoids excessive costs and doesn't aggravate inflation.

He spoke for only a few minutes, refused to answer questions and said he would elaborate this morning when he and White House domestic affairs director Stuart E. Eizenstat present the president's long-awaited health insurance principles.

The principles were promised for yesterday, after being promised again and again and delayed for months, but the unveiling was delayed until today, while the president and Kennedy met yesterday morning in what Kennedy called a last effort to reach agreement.

"We have been unable to reach agreement on two areas that go the heart of the issue," Kennedy reported.

First, he said, "we agreed" to step-by-step phasing-in of complete national health insurance, but "asked for a commitment to a single bill" to phase in various groups of citizens or kinds of coverage over the years, rather than separate bills step by step, which would be "conquered by the special interests with overflowing war chests."

Second, Kennedy said, "We recognized that adjustments would be desirable or inevitable as unforseen events affected . . . future phases," but "we asked for a commitment to oppose any automatic trigger that could kill the program arbitrily" if certain economic or health cost or other conditions were not met.

On both issue one and issue, two, Kennedy said each time, "the president declined to make that commitment."

The president's advisers have also been arguing for months over health insurance. Califano and Eizenstat, by most reports, favored honoring Carter's many commitments to a total or comprehensive health plan, though Califano also opposed introducing it this year.

Carter's economic counselors, led by Charles L. Schultze, chairman of the Council of Economic Advisers, argued for a limited, or "targeted" approach that might start with the poor and the catastrophically ill. They also wanted phase-by-phase conditional "triggers" that would add new coverage only if economic conditions were right and presently skyrocketing health costs were being contained.

By yesterday's accounts, the economic advisers seem to have won. Administration and other sources said Carter's principles will promise, in large vague language, "comprehensive" and "universal" insurance, but insurance to be phased in only under certain conditions.

The principles will promise a role for the private health insurance industry in providing the coverage, it was reported, but will not firmly pledge strict federal regulation of the firms to assure broad benefits and limited profits - other points on which Kennedy and labor wanted assurance.

Finally, Kennedy and labor have apparently been denied another element they wanted - a promise of a more detailed plan quickly enough for Kennedy to open hearings of his Senate health subcommittee after Labor Day. Labor forces badly wanted to start a national campaign for health insurance before the fall election. They wanted to make support for health insurance a condition for labor backing of congressional candidates.

Many members of Congress have told the White House they are cool to this idea. And Kennedy conceded yesterday that if a national health insurance plan went to the Senate floor today, "I'm not so sure we could pass it."

But he said he and his coalition colleagues will again begin working on their bill with "the toughest cost controls you can imagine." and when "working people" and "business people" and others realize that only such a plan can assure care and control costs, "they will support it."

The President's conditional approach, he maintained, would "subvert" any plan from the start and make it "self-destruct," since the doctors and hospitals it is designed to control could run up costs to prevent its expansion.

Meany, AFL-CIO Secretary-Treasurer Lane Kirkland and - in Detroit - United Auto Workers President Douglas Fraser all, like Kennedy, used the word "disappointment" in commenting on the president's decisions.

"Every industrial country except the United States and South Africa has national health insurance," Meany said. "And I don't like to be put in the company of South Africa."