Thirty-four members of the Carter administration, including the entire Cabinet and White House senior staff, offered to resign yesterday in another stunning development in President Carter's effort to revive his presidency.

The dramatic mass resignation offers, which sources said had been under consideration for several days, were made during a series of meetings at the White House with the Cabinet and Carter's top aides.

White House officials said the president will act on the resignation offers "in the next few days." One senior official said Carter is likely to accept some of the offers, both from Cabinet members and from his own staff.

The White House quickly put out word that the resignation offers of the president's "national security team" - Secretary of State Cyrus R. Vance, Defense Secretary Harold Brown and national security adviser Zbigniew Brzezinski - would not be accepted.

But there was no official word on any of the others, only intense speculation as Carter continued the extraordinary process begun two weeks ago when he abruptly canceled a scheduled energy address and convened a "domestic summit conference" at Camp David.

There were conflicting versions of how the resignation offers came about. Three Cabinet officials said that Carter asked for the resignations during a meeting with his Cabinet at the White House.

But a senior White House official flatly denied this, although he conceded that the president was the first to raise the subject during a discussion of the performance of administration personnel.

Speculation on Cabinet dismissals has centered so far on Energy Secretary James R. Schlesinger Jr., Treasury Secretary W. Michael Blumenthal and Health, Education and Welfare Secretary Joseph A. Califano Jr., all of whom have powerful enemies in the White House. Schlesinger said publicly yesterday - before the Cabinet meeting - that he intends to leave the administration this year, probably in the fall.

The president met yesterday morning with his senior staff aides and separately with the Cabinet amid speculation about a shakeup in the administration as a result of the Camp David discussions. But there was no forewarning of the stunning announcement that White House press secretary Jody Powell made to reporters in late afternoon.

"The president had serious and lengthy discussions with his Cabinet and senior White House staff about the priorities of his administration," Powell said."He reviewed with them the progress of the past few years and the problems that remain.

"All members of the senior staff and Cabinet have offered their resignations to the president during this period of evaluation. The president will review these offers as resignation carefully and expeditiously."

It remained unclear last night why Carter decided to extract resignation offers from his staff and Cabinet rather than simply making individual changes. The action was interpreted in some quarters as a further sign of instability in the administration.

The only explanation offered by a senior White House official was that it was thought "appropriate in this period of evaluation," suggesting that those who offered to resign wanted to give Carter as much freedom as possible in remaking his administration.

The action, however, may have been an attempt to reinforce the image of a chief executive firmly in control.

Later the White House issued a complete list of the officials who offered their resignations.It included, in addition to the 12 department secretaries of the Cabinet, three officials with Cabinet rank - Budget Director James T. McIntyre, Special Trade Ambassador Robert S. Strauss and Ambassador to the United Nations Andrew Young.

The 19 White House aides who offered to resign included not only Carter's most trusted advisers, such as Powell, but three members of First Lady Rosalynn Carter's staff and Vice President Mondale's chief of staff, Richard Moe.

It remained unclear last night how extensive a shakeup in the administration Carter has in mind. A White House official said that discussions of the mass resignation offers have been going on for several days among some Cabinet officials and some senior White House aides.

The official said that the president was aware of the ideal and approved it, suggesting that he already has decided whom he wants to replace in the White House and the Cabinet.

From a variety of sources, this picture of the day's extraordinary developments began to emerge by last night:

At 8:30 a.m. yesterday, Carter met with his most senior White House advisers, including Powell, political adviser Hamilton Jordan and domestic policy adviser Stuart Eisenstat.

"The president made it clear that he was reviewing the performance of the entire administration," one official said. "He also made it clear that he was not satisfied - that the performance was not up to par."

There was a discussion of resignations, but no resignations were offered formally at the meeting, the official said.

At 10:30 Carter convened the Cabinet meeing. According to Cabinet sources, he asked for the resignation offers during a discussion of a White House evaluation of high-ranking adminstration officials.

The White House version disputes this, with one official asserting the resignations were offered "spontaneously" with on prodding from the president.

Secretary of State Vance, by protocol the senior member of the Cabinet, was the first to speak on the subject after Carter, sources said. According to one Cabinet source, Vance told the president, in effect, "You don't want them [resignations] in writing, you want them orally." According to the White House version, Vance told Carter he should not have to ask for resignation but the Cabinet instead should offer them.

After that, the sources said, each secretary in turn, around the table in the White House Cabinet room, orally offered his or her resignation.

Yesterday afternoon, a second White House staff meeting was convened, involving not only the most senior aides but most of those who eventually offered to resign. The president was not at the meeting, which was led by Jordan.

The staff aides were told of what the Cabinet had done and, according to one official, "everybody agreed" that they should do the same. Again, the resignation offers were tendered orally, with nothing put in writing.

Later in the day. Jordan placed a conference telephone call to the Cabinet officials, reading to them the White House statement that Powell was about to release to reporters.

Jordan's role throughout the day reinforced the expectation that he has emerged as the White House strong man and is soon to be given the power, possibly even the title, of chief of staff. Jordan not only headed the meeting where the White House staff resignations formally were offered, but was the only White House aide who attended the Cabinet meeting.

Reaction to the day's developments was swift and generally negative. Republican presidential candidate George Bush said, "If there is a lack of confidence in government it is the fault of Mr. Carter's policies, not the men and women entrusted to carry them out."

Another GOP presidential candidate, Rep. John B. Anderson of Illinois, said hte resignation offers were "orchestrated" and they "add instability to the atmosphere."

Rep. Paul Simon (D-III.) said the action makes the president "look like he is in charge" but also "may project an appearance of instability."

The White House announcement was timed carefully so that it came after all major world financial markets were closed for the day. The quick word from the White House that Carter's chief foreign policy advisers would remain in the administration also clearly was intended to soothe the nerves of officials in foreign capitals.

There was no question that the dramatic offer was planned in advance by at least a handful of White House aides with Carter's approval, although some in the Cabinet and White House staff may not have known they were about to offer their resignations until yesterday.

Vice President Mondale, travelling in the Mideast yesterday, said that when the president was at Camp David he discussed "substantial changes" in the administration, involving his own staff, Cabinet and other executive department officials.

Mondale said he talked with Carter about personnel changes last week and knew in advance that the resignation offers would be made.

Asked at a news conference whose idea it was to obtain the offers of resignation, Mondale said, "The president's." He paused and added: "And of course other members of the Cabinet."

There also was no question that yesterday's development were the most visible in the president's effort to restructure his leadership style and the performance of his beleaguered administration. But like the Camp David "domestic summit," the developments also raised expectations.

It remained unclear last night how Carter will follow through and how extensive a shakeup he contemplates. There were no signs that any of his senior White House advisers from Georgia and his campaign days are in danger and some, such as Jordan, appear to have been strengthened. One source said that White House congressional relations chief Frank Moore, probably the most criticized of the senior advisers but a Georgian, would remain at the White House.

Some of the lower-level aides who offered their resignations yesterday - among them Rosalynn Carter's press secretary, Mary Hoyt, and Hugh Carter Jr., the keeper of the White House staff budget - have been criticized privately by other officials. But their departures from the White House would hardly be considered major.

One source said Carter had demanded that Cabinet members obtain resignation offers from the subcabinet, but this was denied by a senior White House official.

Amid the speculation about possible personnel changes, there also were reports that Carter intends to change other aspects of his presidency. One Cabinet official said that during the Cabinet meeting the president complained about the "negative" attitude of the Washington press corps and said he intended to change his pattern of holding regular news conferences.

What added to the surprise of yesterday's developments was Carter's record as a personnel manager, despite his vow at the end of the Camp David summit to "restructure" the administration. Through 2 1/2 years as president, Carter has fired no senior official. Pending the next days' developments, his original Cabinet remains intact, a record of longevity for modern administrations.

When the president announced the appointment of each of the Cabinet officials, he described them in extravagant terms, calling each "superb" in his or her field. He also made each of the Cabinet and senior staff appointees sign a letter pledging to remain in office through his full four-year term. CAPTION: Picture, Secretary of Housing and Urban Development Patricia Harris gestures and says no comment after White House meeting. UPI