President Carter outlined the secret hostage rescue plan in detail to Senate Majority Leader Robert C. Byrd (D-W.Va.) last Wednesday, but did not tell him the attempt already had begun 13 days before, Byrd said yesterday.

Carter said he thought chances for success were "better than 50-50, reasonably good," Byrd told his regular news conference.

Byrd advised Carter yesterday to come out of the White House and begin campaigning for reelection.

Other congressional reaction continued mixed. Senate Minority Leader Howard H. Baker Jr. (R-Tenn.) was supportive, saying only that Carter "should have done this a long time ago . . . . I'm sorry it failed."

But others called for congressional probes of both the equipment failure that caused the mission to be aborted and a possible violation of the 1973 War Powers Act, which requires presidential consultation with Congress prior to certain military actions.

Campaigning virtually ceased in Michigan, where Sen. Edward M. Kennedy (D-Mass.) and other presidential challengers called on citizens to unite behind Carter.

"This is the time for us as a nation and a people to stand united," said Republican front-runner Ronald Reagan. It would be inappropriate to express any other reaction now, he said.

Kennedy flew back to Washington for a briefing on the situation.

Whatever our other differences, we are one nation in our commitment to the hostages, our concern for their families and our sorrow" for the eight men killed in the rescue attempt, he said.

Byrd said he was "puzzled" that Carter had not told him the rescue effort was under way after having invited him to the White House study for an hour-and-45-minute general discussion of the Iranian situation.

"I don't know what his reason was," the West Virginia Democrat said. "I was under the impression it was not something that was imminent, and that there would be an opportunity down the road to consult on it."

He told the president, Byrd continued, that it might be wise to delay any covert action until new sanctions and support from our European allies had taken effect. "'No' he said, 'No, it can't wait that long,'" Byrd related.

Byrd said he had told the president there should be consultation with "a minimum number" of Senate and House members from both parties before any covert action. "I thought there would be support, and that the burden would be spread around, and that such support in the event of failure would be comforting," Byrd said.

He did not think consultation was required under the War Powers Act for this kind of mission, however, he said.

"In my mind [carter] did not act illegally" since the resuce attempt was not intended to take territory, to kill Iranians or use threats or force against the government, Byrd said.

Mining Iran's harbors or blockading them would definitely require prior notification under the act, however, Byrd said. The war Powers Act was passed in 1973 over President Nixon's veto and requires consultation with Congress before military units are sent into most situations that could require combat. "The vergiage can be argued," Byrd said, "but in spirit and intent I don't think there was any violation."

He said he had received more detail on the operation from Carter than had so far been revealed elsewhere. "I wouldn't have given it a 50-50 chance myself, but then I don't know all the details," he said.

He added that in his opinion the event "demonstrated unequivocally to the Soviet Union . . . that this country will act and this president will act and ought not to be taken lightly."

He called on Carter to "get out in the country and hear what people are saying, let 'em hear what he's saying" and not remain "the hostage of the ayatollah" by campaigning from the Rose Garden.

He added that the Armed Services committees should probe reasons for the helicopter mechanical failures and the collision that aborted the rescue mission.

However, the Justice Department said Friday that Attorney General Benjamin R. Civiletti had advised Carter during the last 10 days that he had the power to order such a mission without violating the act. "It took place in an emergency setting . . . and was consistent with the general legislative intent of the War Powers resolution," a spokesman said.

Several members of Congress noted that Carter would have been a hero had the attempt succeeded: Sens. Claiborne Pell (D-R.I.), George McGovern (D-S.D.) and Alan Cranston (D-Calif.), and House Majority Leader Jim Wright (D-Tex.).But Rep. Henry S. Reuss (D-Wis.) was angry: "President Carter should now announce that he is not a candidate for reelection and quietly serve out his term without any more impulsive actions," Reuss said.

The New Democratic Coalition, which describes itself as a group of liberal Democratic activists and office-holders in 30 states, went further than that. The group called on Carter to resign unless he reverses his "militarized, confrontational and secretive policy on Iran."

The coalition accused print and broadcast media of "fanning the flames of U.S. public opinion" so as to turn the situation into an international crisis.