President Reagan drew strong bipartisan support yesterday for his tough military response to Libyan leader Muammar Qaddafi as lawmakers urged close consultations on the crisis but generally avoided pressing the White House to invoke the War Powers Resolution.

The response appeared to go beyond the normal support accorded a president in the early phases of a military action, in part, some Democrats said, because of outrage over Qaddafi and what they called his "outlaw" behavior.

Even House Foreign Affairs Committee Chairman Dante B. Fascell (D-Fla.), who suggested earlier that the president may have violated prior-consultation requirements of the post-Vietnam war powers legislation, said he "fully supported" the U.S. military moves.

The president, he said, had "absolutely no choice" in doing what he did to "preserve the principle of international waters."

Fascell said he did not quarrel with the "president's behavior," only with his failure thus far to invoke the war powers act, which requires formal notification of Congress within 48 hours of hostilities and gives lawmakers 90 days to disapprove any emergency action. "It is absolutely essential the Congress be brought in," Fascell said.

House and Senate leaders were briefed late Monday, several hours after U.S. warplanes counterattacked in what officials said was a response to Libyan missile assaults on Navy aircraft. Administration officials held lengthy, closed-door briefings yesterday afternoon for all members of Congress.

This appeared to satisfy most congressional demands for consultations, and few Democrats or Republicans joined Fascell in pressing the issue of the 1973 War Powers Resolution, which was a major dispute when U.S. troops were involved in Lebanon several years ago in a more controversial role.

Presidential spokesman Larry Speakes said Reagan is considering invoking the law. The 48-hour notification period would run out this afternoon.

Earlier yesterday, Senate Majority Leader Robert J. Dole (R-Kan.) said administration officials do not think that the law applies "at this point" and indicated his agreement. Senate Minority Leader Robert C. Byrd (D-W.Va.) earlier took the same position. "They're going to continue to consult with us and follow the act if necessary," Dole said.

In the House, Majority Whip Thomas S. Foley (D-Wash.) said Congress should focus on "what happens now," rather than a previous failure to consult.

Asserting that the "right of passage in international waters is a foundation stone of American foreign policy since the founding of the Republic," Foley said the Democratic-controlled House was behind Reagan in his response to Qaddafi. "My firm belief is the House would provide overwhelming support."

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) endorsed the president's policy in a statement late Monday and made no mention of the war powers act.

The most outspoken critic of the U.S. move against Libya was Sen. Mark O. Hatfield (R-Ore.), who called it "mindless" and said the United States is "engaging in childlike games of 'dare and double-dare' with a sick and dangerous clown." Hatfield, Appropriations Committee chairman, frequently dissents from administration policy on military issues.

Others who are often critical of the administration were supportive or ambiguous.

Sen. Gary Hart (D-Colo.), seen as a leading contender for the Democratic presidential nomination in 1988, said "defensive actions taken in response to hostile threats are wholly appropriate under such circumstances" but added, "We should know whether our policy is directed to eliciting further responses from the Libyan government."

Sen. Howard M. Metzenbaum (D-Ohio) said there is "no alternative but to respond in kind" when American planes are fired upon but said the United States should now try to "defuse the situation rather than escalate it."

Dole said that any provocation came from Libya, not the United States, and asserted that Qaddafi is now on notice that "we will respond -- in kind, at the source and with effect." Dole added: "From now on, if Qaddafi wants to play, he will pay."