President Reagan said yesterday "we're negotiating hard" with the Soviet Union in Geneva to reduce offensive nuclear weapons and insisted that "talking about a safer world is not good enough. We must make it happen."

In his weekly Saturday radio address from Camp David, Md., Reagan said he is "examining" the recent Soviet proposal for a 50 percent reduction in nuclear arms, but he did not say whether he will heed the advice of the allies last week that the United States respond to the Soviet proposal before the Nov. 19-20 summit with Soviet leader Mikhail Gorbachev. He said his talks with five western leaders in New York "convinced me more than ever that we are on the right track."

At the same time, Reagan challenged the Soviets to disengage from conflicts in Afghanistan, Angola, Cambodia, Ethiopia and Nicaragua, as he did last week at the United Nations. He vowed the United States "shall not cease" backing "resistance forces" fighting Soviet-backed regimes.

Reagan also declared that he is "determined to move ahead on research and testing of our Strategic Defense Initiative," his proposal for a space-based shield against nuclear missiles. The Soviets have attempted to block the plan.

An authoratitve administration source said there is little expectation within the White House of any deal with Gorbachev at Geneva involving limits on SDI in exchange for deep reductions in Soviet offensive missiles. While such a trade-off seemed possible two months ago, the idea "is dead in the president's mind," the source said.

Reagan has publicly ruled out such a trade-off, but some officials had held out hope earlier that he was taking that hard-line position solely for negotiating purposes.

Yesterday's radio speech and Reagan's U.N. address were part of an effort to illustrate a link between Soviet behavior in the Third World and arms-control issues.

But the speeches also highlighted shifting White House tactics for what has become one of the Reagan presidency's most important, high-stakes public-relations campaigns.

The president's strategists concluded in recent weeks that the Soviet propaganda drive before the summit was highly sophisticated and is likely to remain so under Gorbachev. In particular, the Gorbachev proposal for a 50 percent cut in nuclear weapons and the earlier "Star Peace" address to the United Nations by Foreign Minister Eduard Shevardnadze suggested to U.S. planners a degree of sophistication in Moscow's approach that they had not seen in recent years, according to a senior strategist helping plan the U.S. response.

This strategist, who asked not to be identified, said it appeared the Soviet effort could have a long-term effect on world opinion, although it had not shown up yet in the United States, where polls show distrust of the Soviets continues to run deep.

U.S. officials concluded that the Reagan response would have to be skilled and consistent, and they brought in one of the most highly-respected presidential speechwriters, Kenneth L. Khachigian, to draft Thursday's U.N. speech.

They also decided, the strategist said, that Reagan must avoid any embarrassing verbal blunders, such as his recent impromptu statement that seemed to recognize the Palestine Liberation Organization, which he later withdrew, in the midst of the hijacking of the cruise ship Achille Lauro. Such gaffes in the past have overshadowed Reagan's prepared messages.

To this end, Reagan last week took the unusual step of not answering a single question posed to him in "photo opportunities" while meeting western leaders in New York, saying he had made it a "rule" not to answer. One result was that when Shevardnadze came to call, the president would say nothing, but the Soviet foreign minister answered a few queries about Reagan's U.N. speech, saying, "If there were no positive seeds, we would not have met at all."

Shevardnadze was borrowing a phrase out of Reagan's address that the Soviet arms proposal included "seeds that we should nurture."

Officials said they concluded Reagan's rhetoric before Geneva would have to be "measured," not extreme. Aides said last week's speech was originally drafted with more provocative language but was toned down, in part by the president and in part by political and National Security Council advisers.

One result was a speech blending sharp criticism of Soviet expansionism with a "peace initiative." According to the strategist, opinion polls suggest Reagan can risk being blunt about the Soviets when he couples it with proposals for settling disputes or reducing arms.

Rep. Stan Lundine (D-N.Y.), who delivered the Democratic response to Reagan's address, questioned the administration's arms-control commitment. "The real success at those talks will depend on this administration providing genuine leadership towards arms reduction. It's disappointing to see the disarray in the administration. It seems clear that your own team does not agree on the path to sensible arms reduction. Some of them do not even appear to sincerely want a reduction in current arms levels."