Secretary of State George P. Shultz yesterday defended the Reagan administration's record on curbing the spread of nuclear weapons, arguing that promoting nuclear power sales had helped restore U.S. influence in nuclear matters.

"Our efforts have not been widely noted," he told a luncheon gathering of the United Nations Association, a private educational group focusing on international affairs.

He described recent arms sales to Pakistan, the provision of U.S.-controlled plutonium to Japan and the opening of nuclear "constructive engagement" with South Africa as part of a policy "designed to facilitate cooperation with our allies and to ensure us an effective leadership role in international nuclear affairs."

Saying that the world nuclear arms family has held steady at six nations for a decade, Shultz said "our nonproliferation policy has been a success" in terms of decisions by other countries to forgo "destabilizing options" and to accept voluntary constraints.

The speech apparently sought to blunt concern among the 124 other signatories of the International Nuclear Nonproliferation Treaty that the United States has seriously weakened the pact by fostering some nuclear technology transfer and failing to make nuclear arms reductions.

"We must make rational distinctions between close friends and allies who pose no great proliferation risk and those areas of the world where we have real concerns about the spread of nuclear weapons," Shultz said. "A policy of denial toward countries with excellent nonproliferation credentials would be arbitrary as well as counterproductive."

Shultz said policies of the Carter administration showed "a negative attitude" toward nuclear power in trying to discourage plutonium technology and spent nuclear fuel reprocessing. In Japan, which is about to receive a record-size shipment of U.S.-controlled weapons-grade plutonium, and in Western Europe, Shultz said, "nuclear power is critical to national well-being and energy security."

He said the administration's $3.2 billion aid package for Pakistan was an example of efforts "to reduce the motivation of some states to acquire nuclear explosives by working with them to improve regional and global stability."

Critics have charged that Pakistan has not visibly slowed its apparent effort to develop nuclear weapons and argue that the 40 F16 fighter jets in that U.S. aid package could provide Pakistan with a bomb-delivery system.

Shultz noted that the United States has "restored a dialogue" with Brazil, Argentina and South Africa, which have all avoided signing the nonproliferation treaty and appear to be moving toward nuclear weapons production, according to a Carnegie Endowment study released this week.

The United States opposed as "counterproductive" a resolution by the International Atomic Energy Agency in October demanding that South Africa submit its nuclear facilities to safeguards and calling for an international ban on nuclear trade with South Africa. The resolution passed on a vote of 57 to 10.