President Reagan has asked Soviet leader Mikhail Gorbachev to extend the current round of arms control talks in Geneva beyond this week so the United States can present a new proposal that would sharply reduce the nuclear arsenals of both superpowers and require deep cuts in Soviet land-based intercontinental ballistic missiles, administration sources said yesterday.

The sources said U.S. negotiators in Geneva will present the "comprehensive" U.S. proposal to the Soviets on Friday, the last scheduled day of the current round of nuclear arms negotiations. The U.S. counterproposal was described by Reagan yesterday in a letter to Gorbachev, according to a senior administration official.

The sources said it is uncertain whether the Soviets will agree to keep the talks in Geneva open beyond Friday for further discussion of the new U.S. proposal but they have agreed to accept the presentation.

The U.S. plan comes in response to the Soviet proposal for a 50 percent cut in nuclear weapons, which was criticized by the administration as one-sided, but which Reagan has also said included "seeds to nurture."

The sources said the U.S. response calls for a limit of 3,000 warheads on intercontinental ballistic missiles (ICBMs) for each superpower. Currently, the Soviet Union has about 8,900 such warheads, with 6,400 warheads on land-based missiles and 2,500 on sea-based weapons. The United States has 2,130 warheads on land-based ICBMs and 5,370 on sea-based weapons.

The sources said the U.S. proposal sets separate limits on bombers and air-launched cruise missiles, which were not disclosed.

The U.S. proposal will be explained by Secretary of State George P. Shultz on his trip to Moscow early next week, and will also be promoted in Reagan's scheduled address to the nation before he leaves for the Nov. 19-20 summit, the sources said.

Reagan, in a British Broadcasting Corp. (BBC) interview broadcast yesterday, said he will propose that the superpowers share technology for missile defenses such as his proposed Strategic Defense Initiative (SDI). The Soviets have attempted to block SDI, but Reagan said "there couldn't be anything better than if both of us came up with it."

Meanwhile, administration officials said that the Soviets, in a recent informal discussion at Geneva, suggested an agreement on intermediate-range nuclear missiles that included as a first step a freeze, beginning Dec. 1, on U.S. and Soviet forces now in the field.

The next stage of the Soviet plan, covering 18 months, would involve a reduction in the number of U.S. single-warhead cruise missiles deployed in Western Europe to between 100 and 120, and the removal of the U.S. Pershing II missiles based in West Germany.

The Soviets would then reduce their triple-warhead SS20 medium-range missile force in Europe so that they had the same number of warheads on their SS20s as were on the remaining U.S. cruise missiles plus British and French missile forces.

Gorbachev said earlier this month that the Soviets are reducing the number of SS20s in Europe to 243, and proposed to freeze the remaining SS20s in Asia. Gorbachev did not specify from what level the reductions would be figured, but it is believed to be about 300 SS20s in Europe.

The U.S. plans to deploy 464 ground-launched cruise missiles and 108 Pershing II missiles, for a total of 572 missiles. Most of the Pershings are deployed along with more than 128 ground-launched cruise missiles.

The Soviet suggestions are under discussion in the administration, but there is no indication that the United States would agree to dismantle the Pershings.

Until now, the administration has opposed counting British and French missiles as part of an overall limitation of western forces to be negotiated with the Soviets.

Officials said that there is "very little disagreement" on the substance of the U.S. response to the Soviet proposal for a 50 percent cut in nuclear weapons, but timing and format were still being debated early yesterday.

The primary U.S. objections to the Soviet proposal was that it counted medium-range missiles deployed by the United States in Western Europe, including bombs on fighter-bombers, as "strategic" weapons.

The U.S. response will eliminate all medium-range weapons from the count of strategic missiles, officials said.

White House spokesman Edward P. Djerejian had "no comment" on the U.S. response.