Secretary of State George P. Shultz said yesterday that the United States and the Soviet Union agree there is a "relationship" between the three forthcoming sets of arms negotiations, and he acknowledged that it "very much remains to be seen" whether failure in one set of talks could block progress in the others.

Shultz, interviewed on NBC's "Meet the Press," reacted cautiously to Soviet Foreign Minister Andrei A. Gromyko's Moscow statement at a news conference yesterday that he had told Shultz at their Geneva meeting last week that agreements on the U.S. goal of limiting strategic and medium-range nuclear missiles are not possible without corresponding accords that could force the United States to abandon research into outer-space weapons.

Gromkyo's comments, with their implication that the Soviets want strict linkage between progress in the missile and space weaponry talks, provoked differing responses from Shultz and Defense Secretary Caspar W. Weinberger.

Weinberger, speaking on CBS' "Face the Nation," echoed the attitude of administration hard-liners by charging that Gromyko was trying to introduce "a new element" into what was agreed on at Geneva.

Their statements made clear that failure to resolve the linkage question at Geneva has left persistent differences within the administration about whether the three negotiations have been imperiled by a Soviet attempt to use them to derail President Reagan's Strategic Defense Initiative for space-weapon research.

Shultz, reiterating a point he made at a Geneva news conference last Tuesday after the meeting with Gromyko, conceded that there is a relationship between the various aspects of arms control and said it is too early to tell how the different negotiations will be affected by possible linkage.

"I think it very much remains to be seen," Shultz said repeatedly in outlining his view that a lot of negotiating is required before the chances for agreement in any of the three areas can be assessed.

"I think the fact that there is a relationship between different kinds of arms is something we believe and the Soviet Union does too," he said. But that "certainly doesn't doom any chance at all" of successful arms talks, and "We may seek to link things ourselves. It makes sense to link the things you are talking about."

Shultz underscored this essentially forward-looking, positive approach by revealing that talks are expected to begin this week, "probably with our ambassador in Moscow," about deciding a time and place for beginning the three negotiations. Although Shultz did not elaborate, the United States is known to have advocated that the new talks be held in Geneva starting in March.

His words contrasted with Weinberger's tough response.

"I hate to disagree with Mr. Gromyko before the talks start," Weinberger said, "but that was clearly not a position because the talks in Geneva were talks about the way to start the talks themselves . . . .There was no agreement of any kind, as I understand it, that we would agree to ban or prohibit something that the president holds very dear and regards as one of his highest priorities.

"We specifically refuse to agree to any kind of prior conditions for further talks -- that is to say we must prohibit research while we have the talks. We absolutely refuse to do that," Weinberger added.

Weinberger said the administration intends to move ahead with its plans to begin testing antisatellite missiles in March. Some U.S. officials have said privately, however, that the tests probably cannot begin before June because of technical problems.

Shultz, while also reaffirming the importance that the administration places on developing defensive space weapons that could intercept nuclear missiles targeted against the United States, took the more flexible approach of treating Gromyko's remarks not as a threat or precondition but as an area of disagreement that will have to be thrashed out.

"The relationship between these areas is very much the same thing that the president has been putting forward for some time," he said, noting that as recently as last summer the United States had signified its willingness to accept a Soviet proposal for space-weapon talks if they were expanded to include intercontinental and medium-range missiles.

"It makes sense to look at the relationship between the different things you're talking about," Shultz said. "It also makes sense to look at anything you might agree to in one area and say, independent of these relationships, if it's important enough and in our mutual interest, we should go forward with it. And exactly what will happen remains to be seen."

He also revealed that in Geneva Gromyko made statements to him similar to his statements yesterday. But, Shultz added, "then he proceeded to list a lot of exceptions that represented areas that he thought would go forward if they were agreed to."

Shultz would not identify these exceptions beyond "things that the Soviet Union has wanted." However, U.S. officials have said that Gromyko, in the Geneva meeting, listed as "overriding questions" that would not be subjected to linkage such subjects as possible agreements on a threshold test ban treaty, a ban on nuclear testing and a U.S.-Soviet agreement that neither would be the first to use nuclear weapons in a conflict.

Shultz also intimated that he is likely to go to Moscow for another meeting with Gromyko, saying that for "the broad agenda of U.S.-Soviet relations to go forward," periodic discussions alternated between Washington and Moscow are necessary. U.S. officials have said they do not expect Shultz to make a Moscow trip before March at the earliest.