Soviet leader Mikhail Gorbachev today proposed a 15-year timetable for banning nuclear weapons worldwide and announced that the Soviet Union will extend its ban on nuclear tests for three months.

"We propose that we enter the third millennium without nuclear weapons, on the basis of mutually acceptable and strictly verifiable agreements," Gorbachev said in a 45-minute statement read by an evening news announcer on Soviet television.

Linking his proposal directly to the firm Soviet opposition to the Reagan administration's "Star Wars" plans for a space-based defensive antimissile system, Gorbachev said: "Instead of wasting the next 10 to 15 years by developing new weapons in space, allegedly designed to make nuclear arms useless, would it not be more sensible to eliminate those arms and bring them down to zero?"

Gorbachev announced the sweeping Soviet plan one day before Soviet and American negotiators begin the fourth round of the U.S.-Soviet arms talks in Geneva.

During the third round, which ended shortly before the U.S.-Soviet summit last November, both sides presented plans for nuclear weapons reductions.

At the summit, Gorbachev and U.S. President Reagan agreed to give impetus to the arms control talks.

In a reference to the talks, Gorbachev said the Soviet Union would stand by its summit agreement to accelerate the talks on space, strategic offensive arms and intermediate-range weapons. "We expect the same constructive approach from the U.S. side," he added, "above all on the question of space."

The extensive plan the Soviet leader outlined today took the Soviet proposals in Geneva three steps forward.

First, it established a timetable for the Soviet-proposed 50 percent mutual U.S.-Soviet arsenal reductions.

Second, it called for a follow-up to the 50 percent cuts of up to 100 percent.

Third, it specified that all members of the nuclear club should follow the United States and the Soviet Union in reducing the number of nuclear weapons.

All of the projected nuclear reductions would be conditioned on a pledge against the deployment and use of space weapons by all of the nuclear powers, Gorbachev said.

Moscow's moratorium on nuclear tests, imposed in August and originally intended to expire at the beginning of this year, will continue until April, and perhaps longer, if the United States joins it, Gorbachev said.

Earlier, Soviet officials had said that the ban would end on Dec. 31 unless the United States joined.

"The U.S. administration is once again given more time to weigh our proposals on stopping nuclear explosions and to give a positive answer to them," Gorbachev said.

Washington has said it would not join the moratorium because if nuclear weapons are to provide a deterrent, they must be tested.

The new Soviet plan calls for the five nuclear powers to conduct a step-by-step reduction of their nuclear arsenals in these three stages:

*In the next five to eight years, the United States and the Soviet Union would cut 50 percent of the weapons capable of reaching each other's territory, as proposed by the Kremlin last October.

This stage would include reaching an agreement on eliminating intermediate-range weapons in Europe by both superpowers and the retention, on each side, of no more than 6,000 warheads, Gorbachev said. It would apply to both ballistic and cruise missiles, he said.

It would also include a superpower nuclear test ban, he said.

*By 1990, the two superpowers would begin a reduction of their intermediate-range nuclear weapons, while all five nuclear powers would eliminate tactical nuclear missiles that have a range of up to 600 miles. This period would take five to seven years, Gorbachev said.

*By 1995, all of the nuclear powers would begin eliminating all remaining nuclear arsenals. "By 1999, there would be no nuclear weapons on Earth," the Soviet leader said.

"Special procedures will be worked out for the destruction of nuclear weapons," he said.

Gorbachev added a grab bag of previous Soviet proposals. For example, he indicated a willingness to agree to verification by national technical means, through on-site inspections, and said that "the U.S.S.R. is ready to reach agreement on verification through any other verification measures."

The Soviet leader also reiterated his support for stepping up talks to eliminate chemical weapons and for Soviet and U.S. troop reductions in Europe.

By so adamantly supporting far-reaching arms control proposals -- including some for which the United States already has expressed distaste -- Gorbachev is mounting an appeal for arms control activists in the United States and Western Europe to back the Soviet position, according to western diplomats here.

Predicting U.S. objections, Gorbachev said that "possible references to verification as an obstacle" for a nuclear test ban would be "groundless." He added, "verification is no problem as far as we are concerned.

"What is required here is rising above national selfishness, tactical calculations, differences and disputes," he said.