Sen. Patrick J. Leahy (D-Vt.), vice chairman of the Senate Select Committee on Intelligence, said yesterday that he has begun an independent inquiry into a half-dozen CIA operations, including a counter-terrorism program that was canceled after an unauthorized car-bomb blast last March killed more than 80 persons in Beirut.

Leahy said he wants to know more about several sensitive operations and seeks more details on others about which he feels the committee wasn't fully informed.

"We're going to review six to seven operations on our own," he said.

Leahy said he did not know of the counter-terrorism plan in Lebanon, but when asked about it last month, he made inquiries "and found out about it on my own." He refused to give further details.

By law and by agreement with the Reagan administration, the chairmen and vice chairmen of the Senate and House intelligence committees are to be informed of all covert CIA activities. An administration source insisted that the committees had been fully informed, both orally and in writing, of all covert or otherwise sensitive operations.

The Washington Post reported yesterday that President Reagan approved the plan late last year directing the Central Intelligence Agency to train foreign teams to make preemptive strikes against terrorists.

The plan was rescinded after members of the unit hired others to set off, without CIA approval, a car bomb that killed more than 80 persons on March 8, the sources said. The target, a suspected terrorist leader, escaped unharmed.

"Things have fallen between the cracks," Leahy said. "I do not want my side to get caught on a Nicaraguan-mining type problem."

A CIA operation to plant mines in harbors in Nicaragua caused controversy last year because several members of the intelligence oversight committees claimed CIA Director William J. Casey had not told them enough about the operation.

Leahy said he feels Casey and other agency officials are willing to answer the committee's questions about any matter. But he said nothing is volunteered if the questions are not framed exactly right.

Leahy said he told other committee Democrats last week that the inquiry is needed because when he became vice chairman in January, he found that he did not know sufficient details of some of the CIA's most secret and potentially controversial operations.

He declined to identify the other operations.

Leahy said he told the Democrats he is committing his staff to the inquiry and might ask them also to provide staff assistance. The committee assigns staff members to individual senators.

Sen. Sam Nunn (D-Ga.) said yesterday that he was not able to attend Leahy's meeting of Democratic committee members, held last Thursday.

No staff members were present, Nunn said. He added that he would have no comment about Leahy's plan or The Post story.

Leahy said he has good relations with the Senate intelligence committee chairman, David F. Durenberger (R-Minn.), but feels it is necessary to proceed with his own inquiry.

Another committee source said, however, that Leahy and Durenberger have basic disagreements about the use of staff resources and the direction of the committee.

Durenberger could not be reached for comment yesterday. But he said in a recent interview that he hopes the committee will not have to spend much of its time dealing with controversial CIA operations.

He said he wants to shift the oversight role "from putting out fire to fire prevention."

Durenberger said that, in the past, about 90 percent of the committee's time has been spent on intelligence controversies and that he hopes to reduce that significantly.

Administration spokesmen continued to decline to comment on The Post story.

Secretary of State George P. Shultz, in Israel yesterday, said of the story: "I haven't seen The Washington Post today. I do have a very strong view about terrorism, as is well-known. I also have the view that at this stage, actions will speak a lot louder than words, so I don't have anything to say about it."

Shultz, who has made strong public statements about taking action against terrorists, said later that he has decided, for the time being, not to comment on the general subject of terrorism. While Shultz was in Jerusalem, several terrorist bombs exploded there and one was defused.

Robert Sims, deputy White House press secretary, told United Press International, "We never discuss intelligence matters." But he added that The Post story contained "a lot of speculation."

Sources have said Reagan ordered that only the chairmen and vice chairmen of the intelligence committees be notified of several covert operations undertaken late last year, including the antiterrorist training program in Lebanon. There is some question whether all the details filtered down when Durenberger and Leahy assumed leadership of the Senate committee in January.