President Reagan has authorized a Central Intelligence Agency covert operation designed to undermine the Libyan regime headed by Col. Muammar Qaddafi, according to informed government sources.

The plan, which involves CIA assistance to another country or countries in North Africa and the Middle East that oppose Qaddafi, has run into initial resistance from the House and Senate Select Committees on Intelligence, which oversee the CIA. The chairman and vice chairman of the Senate panel recently wrote Reagan to outline opposition to the covert operation.

However, a narrow majority of the members of both panels so far supports the covert action, administration sources said. Secretary of State George P. Shultz appeared before the House committee as recently as last week to support the plan.

The operation, authorized in a formal presidential "finding" signed this fall, is at first designed to disrupt, preempt and frustrate Qaddafi's subversive and terrorist plans, the sources said. Secondly, they said, it might lure him into some foreign adventure or terrorist exploit that would give a growing number of Qaddafi opponents in the Libyan military a chance to seize power; or such a foreign adventure might give one of Qaddafi's neighbors, such as Algeria or Egypt, a justification for responding to Qaddafi militarily.

After 4 1/2 years of ineffective economic sanctions and perhaps some minor financial support or encouragement to Libyan dissidents in exile, the administration has decided that Qaddafi is such an international menace to U.S. interests that covert action should be undertaken, officials said.

Shultz and CIA Director William J. Casey, according to sources, have argued that the new covert plan is designed to stop terrorism, not to support the assassination of Qaddafi.

A longstanding executive order signed by Reagan expressly forbids the CIA or any other U.S. government agency from direct or indirect involvement in any assassination plan.

This is the issue that most concerned the chairman and vice chairman of the Senate Select Intelligence Committee, Sens. David F. Durenberger (R-Minn.) and Patrick J. Leahy (D-Vt.) respectively, who conveyed their opposition to the plan against Qaddafi in a letter to the White House, sources said. In the letter they asked Reagan how the plan would avoid the prohibition against assassination attempts or plans.

The White House responded, sources said, by insisting that there was no plan to assassinate Qaddafi and by asking the two senators to delete the word assassination from their letter. The senators declined to do so, sources said.

Administration sources said there is no doubt that Reagan, Shultz and Casey would like to see Qaddafi toppled, and believe that a support operation costing several million dollars through a third country is the type of antiterrorist operation that can safely and legally be undertaken.

According to intelligence reports, Qaddafi gives support to some 30 insurgent, radical or terrorist groups worldwide, ranging from current hot spots such as Nicaragua and the Philippines to groups in Lebanon, Pakistan, Europe, South America, the Caribbean and Africa, that, reports allege, are pursuing goals contrary to U.S. interests.

A top secret, 29-page "Vulnerability Assessment" done by the CIA and other U.S. intelligence agencies and dated June 18, 1984, concluded that "no course of action short of stimulating Qaddafi's fall will bring any significant and enduring change in Libyan policies."

That 1984 assessment, part of the analysis that led to the decision to launch a covert action now, also concluded that "disaffected elements in the Libyan military could be spurred to assassination attempts or to cooperate with the exiles against Qaddafi."

In light of the executive order banning U.S. involvement in assassination, several sources voiced surprise that the word was used in the vulnerability assessment that was prepared under the direction of the national intelligence officer (NIO) for the Near East and South Asia, the top analyst in the U.S. intelligence community for that region.

The vulnerabilities of the Qaddafi government could only be exploited, according to the assessment, "through a broad program in cooperation with key countries combining political, economic and paramilitary action." It also said that "the exile groups, if supported to a substantial degree, could soon begin an intermittent campaign of sabotage and violence which could prompt further challenges to Qaddafi's authority."

The assessment said Libyan exiles who oppose Qaddafi have received support from Egypt, Iraq, Morocco, Saudi Arabia, Sudan and Tunisia.

The State Department intelligence branch disagreed with the vulnerability assessment and said in a footnote that it "rests too heavily on fragmentary, unsubstantiated reporting and fails to give sufficient weight to Qaddafi's enduring popularity . . . . "

Since 1981, the first year of the Reagan presidency when Qaddafi allegedly dispatched "hit teams" to assassinate the president or other top U.S. officials, Qaddafi has been a thorn in the administration's side.

The president has authority to begin covert operations that he deems necessary for the national security. Under the law, the congressional oversight committees must be informed fully and in a timely fashion. If Congress objects to the operation, the only recourse is to cut off the funds, as was done with the CIA covert operation against Nicaragua.

An alternative to an actual attempt to overthrow Qaddafi, according to sources and documents, might be some paramilitary support to Egypt or Algeria, the chief countries that might be able to bring pressure on Qaddafi, though both have had serious reservations about cooperating with the United States in the past when covert anti-Qaddafi proposals have been discussed.

Last year, according to sources, a covert plan against Qaddafi was blocked by CIA Deputy Director John N. McMahon on grounds that the exiles were "Boy Scouts" and too weak to have even half a chance at success.

Casey supported that decision not to move ahead with a covert operation because no U.S. ally would support it. Last year Qaddafi was gaining some respectability in Europe, expanding intelligence ties with Greece and enhancing military relations with Italy and Turkey, according to intelligence sources.

The sources were unable to explain exactly why the administration has chosen this time to launch the covert operation. But they pointed to a Special National Intelligence Estimate entitled, "Libya's Qaddafi: the Challenge to the United States and Western Interests," completed earlier this year, that said Qaddafi "provides money, weapons, a base of operations, travel assistance or training to some 30 insurgent, radical or terrorist groups."

The report said reliable intelligence showed Qaddafi stirring up trouble worldwide by continuing subversion in Chad, Sudan and Tunisia; pursuing common goals with what the estimate called the "radical states" of Iran, Syria, Ethiopia and Nicaragua, and through continuing support to groups in the Philippines, New Caledonia, Pakistan and Zaire.

A map in the intelligence estimate showed Qaddafi supporting insurgents or terrorist groups in countries such as Guatemala, El Salvador, Chile, Colombia, the Dominican Republic, Lebanon and Iraq.

In addition the map showed Qaddafi providing financial support to the political opposition or to leftist politicians in Costa Rica, St. Lucia, and Dominica.

The estimate said there were 50,000 Soviet and Eastern European technicians or advisers in Libya. Such special or regular intelligence estimates are issued by Casey with input from the other U.S. intelligence agencies.

Calling Qaddafi "a judicious political calculator" and pointedly saying that he was not living up to his madman image, the intelligence estimate said that Qaddafi would continue to be a threat to U.S. and Western interests.

Early this year some Libyan military officers launched two unsuccessful assassination attempts against Qaddafi, who responded by executing as many as 75 officers accused of participating in them.

U.S. intelligence agencies receive almost a steady stream of reports -- many considered reliable -- that Qaddafi is expanding his terrorist capabilities and planning various actions against U.S. installations or individuals.

Earlier this year one report said Qaddafi had formed two new special operations units to conduct commando and terrorist operations, including one naval unit headed by a senior aide.

Within the last two weeks there have been intelligence reports that Qaddafi was targeting the U.S. Embassy in Tunis and the U.S. ambassador to Tunisia, according to government sources.