President Reagan has responded to Soviet leader Mikhail Gorbachev's Jan. 15 arms-reduction offers by proposing to eliminate all U.S. and Soviet intermediate-range nuclear weapons worldwide within three years, but suggesting two different ways to do it.

Administration sources said yesterday that a letter from Reagan outlining his proposals has been dispatched to Moscow in time for Gorbachev to receive it before the opening of the Soviet Communist Party Congress on Tuesday.

The new U.S. positions are outlined in general terms in the letter to Gorbachev and conveyed in greater detail in new instructions sent over the weekend to U.S. negotiators in the Geneva arms talks, officials said. Reagan adopted his positions in a meeting with top advisers aboard Air Force One returning from Grenada on Thursday, following lengthy discussions within the administration and week-long consultations with U.S. allies in Europe and Asia by senior arms advisers Paul H. Nitze and Edward L. Rowny.

Gorbachev's Jan. 15 offers, which called for elimination of all nuclear weapons of all types by the end of the century, caught the administration by surprise. While Reagan's immediate reaction was positive, there was much internal debate about how to respond, especially to the intermediate-range nuclear force (INF) offers, which seem to hold the promise of an actual agreement within coming months between the two nuclear superpowers.

Gorbachev's INF offer was taken even more seriously in Washington after the Soviet leader told Sen. Edward M. Kennedy (D-Mass.) Feb. 6 that an agreement in this area could be made regardless of whether there was any progress toward accord on reducing strategic nuclear weapons or banning an arms race in outer space.

The Soviet leader also told Kennedy that his decision about whether to come to Washington this June or July for another summit meeting with Reagan, as the United States has proposed, would depend on whether major progress could be made in the meantime toward an INF agreement or a comprehensive ban on nuclear weapons testing.

By calling for elimination of INF missiles both in Europe and Asia within three years, Reagan is outpacing Gorbachev's Jan. 15 proposal that U.S. and Soviet intermediate-range forces be eliminated from Europe within the next five to eight years. Officials said that by doing so, the administration hopes to regain the public relations initiative, even while proposing a phased process of reductions that takes account of unexpectedly strong misgivings expressed during the recent consultations by western European allies and Japan.

Reagan did not accept the two major conditions placed by Gorbachev on his INF offer Jan. 15 -- that the United States agree not to transfer medium-range or strategic missiles to other nations and that Britain and France agree not to increase their small nuclear arsenals. Reagan told Gorbachev that he cannot negotiate for the British and French, sources said.

The two options approved by Reagan for eliminating U.S. and Soviet INF missiles within three years are:

*A phased reductions option, starting with a limit of 140 nuclear launchers on each side in Europe in the first year, a cutback to 70 launchers on each side in the second year and further reductions to zero on each side at the end of the third year. Proportionate reductions would be made in Asia.

*A Europe-first reductions option, calling for elimination of all U.S. and Soviet INF missiles in Europe, and a 50 percent initial cutback in INF missiles in Asia. Soviet INF missiles deployed in Asia in this phase would be limited to bases in the central part of the Soviet Union, from which they could reach China but probably could not reach Japan. The United States could retain an equal number of INF weapons during this period, probably deployed on U.S. territory.

The first option was crafted to respond to North Atlantic Treaty Organization allies who were unhappy at the prospect of agreeing to quickly eliminate all U.S. Euromissiles so soon after the same allies had gone through tumultuous battles at home to authorize their emplacement. The "proportionate Asia reductions" in the first option and the limited Asian deployment zones in the second option were intended to respond to unexpectedly strong worries from Japan that the U.S. proposal could reopen an internal debate there on nuclear weapons issues.