Six Republican senators called for James G. Watt's resignation yesterday as the embattled secretary of the interior pleaded with President Reagan to forgive him for characterizing five advisers as a black, a woman, "two Jews and a cripple."

Reagan accepted Watt's apology, contained in an emotional letter, as adequate. But a White House official said the outcry from Congress and the public may force Watt to step down eventually.

"The jury is still out," the official said. "A lot depends on what the reaction around the country is and how long it lasts."

While the six Republican senators called for Watt's ouster, Majority Leader Howard H. Baker Jr. (R-Tenn.), Finance Committee Chairman Robert J. Dole (R-Kan.) and Budget Committee Chairman Pete V. Domenici (R-N.M.) stopped just short of saying he should resign.

"To me, it's gone on long enough," said Dole, a partially disabled World War II veteran whose views are influential with the White House. "I don't mind the secretary shooting himself in the foot, but I don't think he should continue to punish the president and the Republican Party."

"We will know soon if Jim Watt will survive this goof," Baker said.

Dole and Baker were referring also to past remarks by Watt that angered environmentalists, Jewish leaders, American Indians, fans of the Beach Boys musical group and others.

In the latest gaffe, Watt on Wednesday told a breakfast meeting of business lobbyists that the panel reviewing his coal leasing program has "every kind of mix you can have. I have a black, I have a woman, two Jews and a cripple. And we have talent."

The comment has brought the loudest and most widespread condemnation of Watt since he took office, surpassing the backlashes against his wilderness policies, his offshore oil and coal leasing programs and his confrontational style. Democrats have called for his ouster, but yesterday marked the first time that Republicans have joined them in significant numbers.

The Republican senators calling for his resignation were Commerce, Science and Transportation Committee Chairman Bob Packwood (Ore), Warren B. Rudman (N.H.), Lowell P. Weicker Jr. (Conn.), Alfonse M. D'Amato ( N.Y.), Rudy Boschwitz (Minn.) and Slade Gorton (Wash.).

Rudman, the first to call from the Senate floor for Watt's resignation, termed him "an embarrassment to the president who appointed him, an embarrassment to the party to which I proudly belong and an embarrassment to the country." Rudman later said he received numerous calls from constituents congratulating him for speaking out.

Weicker said Watt "articulates the trash of American thought" and "what one does with trash is what I suggest the president . . . do with James Watt." He called the interior secretary's comments "part of a panorama not of error but of bigotry and hate."

D'Amato called Watt a "colossal bigot," Gorton termed him "a dead bird for the president," and Boschwitz said, "These last remarks have pushed me over the edge" to the belief that the interior secretary should resign.

Domenici said Watt should "reassess his value to the president and the government" in light of his earlier promise to resign if he became a liability to Reagan. Packwood said, "If the secretary doesn't resign, he should be fired."

Amid the furor, Watt sent Reagan a letter seeking forgiveness for the remarks, saying they were "well-intentioned and were not meant to insult or cast a slur upon any groups or individuals." Watt did not offer to resign, and Reagan did not suggest that he do so.

White House spokesman Larry Speakes said Reagan accepted the apology and considers it an adequate answer to the calls on Capitol Hill for Watt's ouster.

"I realize now how easily my statement could be interpreted as morally offensive," Watt wrote to Reagan, in a letter composed after consultation with the White House staff. "I deeply regret that not only because it expresses a sentiment that is entirely wrong in this nation, but is also extraordinarily unfair to you, Mr. President.

"I deeply believe that you are providing moral leadership to this nation and that your policies are designed to lift the scourge of discrimination from our midst . . . .

"I have made a mistake, Mr. President," Watt concluded, closing the letter "with best regards."

Interior officials said Watt believes the controversy is overblown and expects to survive it, as he has several others, by apologizing and avoiding publicity.

"We figure he's survived so much it'll take another Mount St. Helens eruption to blow him out of here," said an official close to the matter.

However, the Republicans who criticized Watt said they do not consider the letter sufficient. Dole said that "there may be an alternative" to Watt's resignation, "but I'm not sure what it is."

Several Republican senators said in interviews that the outcry reflects a growing sentiment that Watt's conduct as interior secretary is harming the Republican Party and the president, both because of his confrontational style and his environmental policies.

During the recent congressional recess, they said, they noticed mounting opposition to him among groups ranging from East Coast fishermen fearful of oil spills to western farmers worried about coal development.

Several of the senators said that, regardless of whether they support or oppose Watt's policies, they believe his latest slip has rendered him ineffective as a spokesman for administration programs.

"Such insensitive remarks . . . greatly minimize the support he can muster for the difficult decisions he must make," Domenici said.

"Mr. Watt clearly is a liability for the Republican Party, more so than in the past," said Sen. John H. Chafee (R-R.I.), chairman of a subcommittee of the Senate Environment and Public Works Committee. "The president is making sincere efforts to solidify groups that have felt alienated from his administration--women, for example--and here Mr. Watt just handles them in the same cavalier manner in which he has handled his coal leasing program."

Sen. Paul Laxalt (R-Nev.), one of Reagan's closest advisers, conducted a private poll of western senators--the bedrock of Watt's congressional support--and found him "weakening," according to Senate aides.

In the last week, Watt suffered a surprising setback when the Republican-dominated Senate clamped a moratorium on his controversial coal-leasing program. Several senators said they were angered by Watt's efforts to accelerate the issuance of leases in North Dakota days before the proposed moratorium was to come to a vote.

"I'll defend him to the death on things that are unfair to him or that I see as loaded and prejudicial against him," said Sen. Alan K. Simpson (R-Wyo.), a longtime friend of Watt.

Simpson's father, former senator Milward Simpson, hired Watt more than 20 years ago as a legislative aide. "But what he said this time is nothing we can imagine as being appropriate, and he knows that.

"Knowing him as I know him, I'm sure he is very pained about this. He is not a robot. He has a heart and a soul just like the rest of us."