Secretary of State designate Cyrus R. Vance said yesterday that he would restrict covert U.S. intelligence operations against other nations to "the most extraordinary circumstances," under tight control.

The foreign policy outlined by Vance would greatly limit what Sen. Frank Church (D-Idaho) called "the black arts of covert operations - bribery, false propaganda, physical coercion, abduction, indeed, attempted assassination of political leaders."

Vance told the Senate Foreign Relations Committee in his confirmation hearing that "I have thought long and carefully about this subject." He then outlined a process that would virtually end what is known as "presidential deniability" or "official deniability" of secret operations to manipulate political events in other nations.

Covert action against other nations, Vance said, "should be carried out only in the most extraordinary circumstances." A foreign operation, as distinct from intelligence gathering, he said, should reguire approval from a Cabinet committee including the secretaries of State and Defense, the President's national security affiars adviser and the Attorney General.

"I think that the President of the United States himself should sign off, in writing, saying that he believes this vital to the national security," said Vance. In addition, he said, advance notice should be given to the proper congressional committee or committees, and if they disagree, while they would not have "a veto," their opposition "would have great weight on any President."

"An adequate monitoring system" should watch and, if necessary, cut off the operation, Vance said.

"I am much reassured," said Church, who was chairman of the Senate intelligence committee, which revealed extensive use of "the black arts" in Chile, Cuba and other nations. The Watergate scandals were an extension of these practices to the domestic scene.

"We must have policies based upon fundamental values," Vance said. "In particular, we must stand up for human rights, without being intervetionists."

Vance said the Carter adminstration will give "greater emphasis" to human rights in dealing with represive regimes, although, he said, "there are cases in which security aspects are of overiding importance."

The low-keyed Vance, peering over half-glasses, was a striking contrast in his first hearing to the man he will replace, Henry A. Kissinger. Vance's confirmation by the Senate is assured. In nearly three hours of testimony, he was questioned only moderately critically by one senator, George McGovern (D-S.D.), about his support of the Vietnam was when Vance was Army secretary and then deputy secretary of defense in the 1960s.

Vance said that "in the light of hindsight, I believe it was a mistake to intervene in Vietman" and I know I made more than my share of mistakes." Lessons learned from the experience, he said, included the error of "trying to prop up a series of regimes that lacked popular support . . ."

The Carter administration, Vance said, does not shun the term "detente," as the Ford administration came to do, but in dealing with the Soviet Union "we should seek a clear understanding on the meaning of detente."

"I do think it is important," he said, "to have a better understanding of what the ground rules are and what we can expect of each other.

"We should pursue the lessening of tensions with the Soviet Union in an active and aggressive way, particularly in the area of reduction and control of nuclear weapons."

Strengthened cooperation with allies, Vance said, "is central to everything else."

Over the long term, hw said the dominant issues will include "control of nuclear arms and nuclear proliferation, economic development and the dignity of the developing world, energy, food, populations, environment and conventional arms transfer." These, he said, "will determine how the next generation lives - and even whether it lives."

Vance said the problems of national and world economics are now so inter-locking that they must be planned for in coordination.

An "economic working group" will be established for this purpose, he said, consisting of the secretaries of Treasury and State, the director of the Office of Management and Budget, the chairman of the Council of Economic Advisers and two White House members, one representing the National Security Council and the other domestic interests.

Vance said that "public confidence in American foreign policy required confidence in how these policies are made." He told the committee headed by Sen. John J. Sparkman (D-Ala), "I will come completely clean with you" and "If I am informed, I will not mislead you."