WASHINGTON (AP) _ The five major navies of the world now have about 16,000 nuclear weapons assigned to them, including roughly 6,500 ''non-strategic'' warheads that are not covered by any type of arms control treaty, according to a new study.

''The nuclear arms race at sea is longstanding, and accelerating,'' the study concludes. ''As of the end of 1987, 1,101 ships and submarines and over 3,250 aircraft (could) fire, transport or service one or more of these nuclear weapons.

''And all of the nuclear powers have ongoing nuclear research and development programs and are producing new naval nuclear weapons, as well as the ships, aircraft and missiles that carry or launch nuclear warheads.''

The study, which focuses on the navies of the United States, Soviet Union, England, France and China, is entitled ''Nuclear Warships and Naval Nuclear Weapons: A Complete Inventory'' and was published today by the Institute for Policy Studies and the environmental group Greenpeace.

It was written by William M. Arkin, the director of the National Security Program at the institute, and a research associate, Joshua Handler. The institute is a non-profit, liberal think tank based in Washington that has frequently criticized the administration's military policies.

Arkin predicted the study could accelerate debate in countries around the world about allowing nuclear-armed ships to make port calls because it lists the individual ships in the five navies that have been certified to carry or fire nuclear weapons.

The 95-page report, by providing such specific information, also is attacking the official U.S. Navy policy of never confirming or denying the presence of nuclear weapons, Arkin said.

''The Navy argument that the policy bolsters deterrence is just baloney'' because the ships certified to carry nuclear weapons can be identified, Arkin said.

''I don't think many people have any idea that there are 16,000 nuclear warheads at sea - one-quarter to one-third of the total in the world,'' he continued.

''But the naval proliferation (of nuclear weapons) is becoming a matter of concern to foreign governments. And I believe there is a growing interest and sense that controls are needed for naval nuclear weapons.''

According to the report, the five navies currently deploy 14 types of long- range ballistic missiles on 17 types of submarines. That combined arsenal of strategic weaponry now totals 1,792 missiles with 9,487 warheads.

On the non-strategic, or short-range, side, the largest single category of nuclear weaponry is deployed for anti-submarine warfare. According to Arkin, there are now 3,300 such ASW weapons in the fleets of the United States, Soviet Union and England.

Short-range nuclear weapons also have been deployed for use against enemy aircraft, other ships and targets on land, the study adds. The United States and Soviet Union so far have deployed a combined 548 nuclear warheads on sea- launched cruise missiles and another 541 warheads on anti-aircraft missiles.

''The U.S. and Soviet navies are the most heavily 'nuclearized' of these nuclear weapons states,'' the study observes. ''Seventy percent of the total U.S. fleet has a nuclear weapons capability, either in a combat or support role, while virtually all of the Soviet Union's principal warships are nuclear-capable.

''The other three fleets have a much smaller proportion ... Some 32 percent of the United Kingdom's; 12 percent of France's, and 2 percent of China's major warships and submarines are nuclear capable.''

Beyond the number of ships that carry nuclear weapons, ''approximately 544 nuclear-powered reactors are located at sea,'' the study found.

''The Soviet Union uses 342 reactors to run its fleet of nuclear-powered submarines, cruisers and ice-breakers. The United States has 169 nuclear reactors (at sea).''