President Reagan has signed a letter to Soviet leader Mikhail Gorbachev welcoming his proposal for an agreement that would ban medium-range nuclear missiles in Europe but calling for a reduction of Soviet missiles targeted on China and Japan, administration offficials said last night.

The president's letter, a response to a Jan. 15 Soviet proposal that calls for the elimination of all superpower nuclear weapons by the end of the century, is scheduled to be sent to Gorbachev early this week. It is likely to be accompanied by a public statement from the White House, officials said.

While the letter describes a prospective ban on medium-range weapons in Europe as a "constructive first step," it does agree to the Gorbachev proposal for an elimination of the weapons unless the Soviets accept a sharp reduction on the same weapons, primarily SS20s, now based on Asia.

Administration officials said that this issue would have to be negotiated at Geneva, where U.S. and Soviet negotatiors are holding separate meetings on three areas of discussion: medium-range missiles, intercontinental strategic ballistic missiles and weapons in space.

Before the Jan. 15 proposal, the Soviets had insisted that U.S. agreement to ban development and testing of Reagan's Strategic Defense Initiative, often called "Star Wars," was necessary before progress could be made in other areas of discussion.

Officials said that in his letter to Gorbachev, Reagan -- while also dealing with the other issues raised in the Soviet proposal -- expresses a positive attitude about the possibility of a separate earlier agreement banning the intermediate-range missiles.

In a Feb. 10 interview with The Washington Post, the president said he was "optimistic" that such an agreement could be signed this year.

Officials said the president will issue revised instructions to the U.S. negotiating team headed by Max Kampelman at Geneva.

Some U.S. officials have said that it is possible that an agreement banning the medium-range weapons could be signed as early as this summer, when Reagan and Gorbachev are scheduled to meet for their second summit.

This would also require overcoming the question of what to do about British and French missiles, which the Soviets had long insisted should be counted in the European totals.

But the Jan. 15 Soviet proposal accepted these missile systems, providing they were not increased.

The U.S. position is that the British and French missile systems are matters for these countries to negotiate separately with the Soviets. But Reagan's letter reflects consultation with both Britain and France, as well as other allies.

"Generally, there is support both in Europe and Asia for the U.S. response," a U.S. official said last night.