President Reagan said yesterday he is "encouraged" by the beginning of "legitimate negotiations" in Geneva to reduce nuclear weapons following last week's presentation of a new U.S. proposal to the Soviet Union.

In his weekly radio address from Camp David, Reagan said, "Now we've had a proposal on the table in Geneva for quite a while. Now, the Soviet Union has offered a counterproposal, and we in turn have a new proposal now reflecting some of the elements of both of the others. And this is what negotiation is all about."

Reagan claimed "our strategy has been working" on arms control, adding, "I believe we have laid the groundwork for productive negotiations in Geneva."

The president said the United States has "accepted" the Soviet proposal for a 50 percent reduction in certain types of nuclear weapons. But he pointed out that the administration is defining the types of weapons to be cut differently from the way the Soviets did in their September offer.

Reagan said the reductions "must be applied to systems which are comparable." This was a criticism of the Soviet proposal, which sought to count all U.S. weapons in Europe but excluded Soviet weapons that can hit Europe.

The president, who sought and received an extension of the Geneva arms negotiations into this week so the U.S. offer could be outlined before the Nov. 19-20 summit, said yesterday the new American response takes into account "expressed Soviet concerns."

He did not elaborate but said the United States has "demonstrated flexibility in taking legitimate Soviet interests into account."

On his proposed space-based missile defense system, the Strategic Defense Initiative, Reagan reiterated that he wants to continue research. "Each of us is pursuing research on such defenses, and we need to be talking to each other about it," he said.