The House Foreign Affairs Committee voted yesterday to supplant the law governing the Central Intelligence Agency's covert operations with a new rule providing for much more secrecy.

Acting on a series of voice votes after a closed-door briefing from the CIA, the committee decided to restrict reports to Congress about covert operations to the Senate and House Intelligence committees, and to allow the president to avoid prior notification when he deems it "essential."

A move to require the president to give at least some vague advance notice of especially risky operations -- without specifying any details -- was beaten down.

It was the first test this year of the Carter administration's drive to get rid of restraints imposed on the CIA in the mid-1970s and provide it with a freer hand in the new Cold War atmosphere.

Rep. Lee H. Hamilton (D-Ind.) had won approval last week from a Foreign Affairs subcommittee of a flat rule calling for prior notice to Congress of all covert operations, but he trimmed it back substantially in the face of opposition from the CIA and committee Chairman Clement J. Zablocki (D-Wis.).

The final version, cosponsored by Hamilton and Rep. Willaim S. Broomfield (R-Mich.), calls for advance notice of covert activities to the two intelligence committees, but with two broadly stated exceptions.

Under the committee-approved measure, "the president may defer, for the shortest practicable period such prior reporting if, at the time the report is given, the president certifies that such deferral was essential to meet extraordinary circumstances affecting the vital interest of the U.S. or was essential to avoid unreasonable risk to the safety or security of the personnel or methods employed."

Hamilton said he meant this provision to be invoked only in highly unusual circumstances, but some members voiced fears that it would become the rule rather than the exception.

"The president can certify these conditions any time he wants," protested Rep. Donald J. Pease (D-Ohio). "We're essentially saying here that whenever the president is so inclined, there can be a covert operation without notification to Congress" for as long as he chooses.

Pease moved to add a proviso that would require the president at least to tell the intelligence committees "that an unspecified covert operation is about to be undertaken," but the idea was rejected.

"It would provide a field day for the press," declared Rep. David R. Bowen (D-Miss.).

Pease vainly sought to remind his colleagues that the notifications themselves are supposed to be tightly guarded secrets. "There's nothing in my amendment that says it would be broadcast to the media or anyone else," he said.

The present law governing covert operations, known as the Hughes-Ryan amendment, was enacted in 1974 as part of that year's foreign aid bill. The Foreign Affairs Committee yesterday approved the new version in the process of marking up this year's foreign aid authorizations.

Under the provisions of Hughes-Ryan, no covert actions in foreign countries can be undertaken "unless and until the president finds each such operation important to the national security and reports, in a timely fashion, a description and scope of such operation to the appropriate committees" of Congress. Eight Senate and House committees, including Foreign Affairs, are entitled to receive those reports under the law, although one of the panels, House Armed Services, has said it doesn't want them.

Yesterday's action would cut the number to two, the traditionally tight-lipped Senate and House Intelligence committees. Rep. Howard E. Wolpe (D-Mich.), arguing that covert operations clearly affect foreign policy, sought to keep the House Foreign Affairs Committee and Senate Foreign Relations Committee on the list, but his colleagues turned him down, again on a voice vote.

Instead, Hamilton said the Foreign Affairs Committee will seek a change in House rules that would entitle it to three seats on the House Intelligence Committee. It currently has one seat, which is occupied by Chairman Zablocki.