Interior Secretary James G. Watt prepared a letter of resignation last Saturday but decided not to submit it to President Reagan after becoming convinced that neither the president nor the White House staff would press him to quit, administration sources said yesterday.

Watt's decision not to resign was based on a judgment that he could ride out the furor created when he described appointees to an Interior Department coal commission as "a black . . . a woman, two Jews and a cripple," the sources said.

Senior White House officials, under instructions from Reagan not to move against Watt, met privately late Tuesday afternoon and agreed that Watt was not going to be pushed from office, at least in the short run. The officials left open the question whether Watt should remain in the Cabinet once Reagan's re-election campaign begins in earnest.

Some administration officials expressed hope that once the storm over Watt's remark dies down Watt would quietly leave the administration to avoid becoming a campaign issue. But they emphasized that there is no specific agreement nor timetable for such a departure.

Presidential spokesman Larry Speakes quoted Reagan as saying yesterday that the Watt controversy is "closed." And Speakes said that "the matter is behind us."

Administration officials said yesterday that the only development that could prod Watt into an immediate resignation would be agreement by a majority of Republican senators to bring to the floor a pending resolution urging Reagan to ask Watt to step down.

The Democratic caucus in the Senate unanimously endorsed the resolution yesterday.

"No Cabinet member can survive a no-confidence vote by the Senate," said one official. A congressional source added, "If you ever get that resolution to the floor, he would not get a vote of confidence in the Senate."

In the House, Rep. Edward J. Markey (D-Mass.) and Rep. Stewart B. McKinney (R-Conn.) introduced a similar resolution.

House Republican Leader Robert H. Michel (R-Ill.), emerging from a meeting between Reagan and GOP congressional leaders, said that the Interior secretary has created a political problem for Reagan and his party.

"Let's face it, these things come up, and it doesn't help matters," Michel told reporters. Asked if the Watt controversy would be a "windfall" for Democrats, Michel said that "could very well be the case." Michel also said that there are other conservatives who could fill Watt's role in the administration.

Former president Gerald R. Ford said in San Antonio yesterday that Watt has become a burden to Reagan and "ought to take action to relieve the president of that burden."

Senate Foreign Relations Committee Chairman Charles H. Percy (R-Ill.) said that Watt has "a duty, an obligation, a responsibility . . . to at least put a letter of resignation on the president's desk" and "then let the president decide."

But administration officials said that Watt, whose confidence that he could stay appeared to be growing, now has no intention of submitting such a letter.

"He doesn't want to leave," said an official. "Reagan has made it clear that he's not going to push him out. Unless the Senate does it, he'll survive."

Last Friday there was a widespread view in the White House, apparently shared by Watt, that the pressures for resignation were nearly insurmountable. Reagan was scheduled to give a major speech Monday at the United Nations and presidential assistants decided late last week to wait out the question of Watt's future until Tuesday.

This had the effect of giving Watt three days of breathing room while his supporters rallied to his defense.

Reagan's top three aides took different approaches.

White House counselor Edwin Meese III, who has the closest ties to conservative activists, strongly backed Watt in a senior staff meeting and questioned the motives of those who wanted Watt out. Deputy chief of staff Michael K. Deaver, who long has considered Watt a political liability to the president, wanted him pushed out. Deaver is said to have had the backing of Nancy Reagan, who has been critical of Watt since he moved to bar the Beach Boys from a July 4 concert on the Mall here.

Chief of staff James A. Baker III, who has been a Watt critic in the past, took no active role in the White House deliberations, sources said, even thought he was criticial of Watt's remark.

The net effect was that the White House staff, which in the past has moved decisively when Reagan's political standing was endangered by personnel crises, was immobilized during the key days when Watt was considering whether to submit his resignation.

Yesterday, some White House officials said that they thought the Watt affair had caused more of a stir in Washington than it had elsewhere.