President Carter's national security adviser, Zbigniew Brzezinski, charged yesterday that "in some measure" the Soviet Union shares responsibility with Cuba for the bloody invasion of Zaire by Katangese rebels.

Describing Moscow's behavior as a "shortsighted attempt to exploit global difficulties," Brzezinski said, "I do not believe that this kind of Soviet-Cuban involvement ought to be cost-free."

"There are a variety of ways in which concerned countries can convince the Soviets and Cubans that their involvement, their intrusion, is not only conducive to greater international instability, but in fact carries with it consequences which may be inimical to them as well," Brzezinski said on "Meet the Press" (NBC, WRC).

His harsh warning continued the drumfire of administration criticism that began last Thursday when Carter publicly accused Cuba of arming and training the rebels who invaded Zaire's Shaba Province from the neighboring Marxist country of Angola.

On Saturday, the administration's concern about Soviet and Cuban activities in Africa led to an open clash here between Secretary of State Cyrus R. Vance and Soviet Foreign Minister Andrei Gromyko.

Gromyko told reporters that the information on which Carter based his charges "is not correct." Later, Vance, with Gromyko standing at the Soviet's remark and said: "The president is fully and accurately informed, and I want to make this very clear."

Brzezinski picked up the theme yesterday, and added that another Sovietally, East Germany, may also have been involved.

"I can assure you that what the president said was right," Brzezinski asserted. "The invasion . . . could not have taken place without the invading parties having been armed and trained by the Cubans and indeed perhaps also the East Germans, and we have sufficient evidence to be quite confident in our conclusion that Cuba shares the political and the moral responsibility for the invasion, indeed, even for the outrages that were associated with it."

He then broadened the charge to include Moscow. "We believe that the evidence we have sustains the proposition - more than that, sustains the conclusion that the Cuban government and in some measure the Soviet government bears the responsibility for this transgression."

He said the administration is willing to make its intelligence available to the Senate.

In a sharp indictment of recent Soviet actions, Brzezinski accused Moscow of "a sustained and massive effort to build up its conventional forces, particularly in Europe: of strengthening its forces on the Soviet-Chinese border; of maintaining "a vitriolic worldwide propaganda campaign against the United States;" of trying "to encircle and penetrate the Middle East" and of stirring up "racial difficulties in Africa."

"This pattern of behavior I do not believe is compatible with what was once called the code of detente," he said bluntly and made explicitly clear that the Carter administration intends some kind of countering action.

In that respect, he reiterated that the administration is chafing under what it considers excessive restraints placed on it by Congress, particularly in regard to possible U.S. actions in Africa. He also increased a notch the pressures now being exerted by the administration to induce Congress to give it a freer hand in the conduct of foreign policy.

The legislative restrictions he argued, "were imposed at a time of very intense suspicion as to the intentions and conduct of the executive branch. They were imposed at a time of the Vietnamese war and Watergate affair."

Then, in what amounted to an indirect assertion that Congress can trust the Carter administration not to abuse its powers, Brzezinski added:

"These conditions have changed. It seems to me that in the light of this change and given the nature of the problems we now confront in some parts of the world, a serious, constructive and the legislative branches about the relevance, the scope of the existing restrictions is timely . . ."

In laying down this line, Brzezinski seemed to be signaling that those in the administration who want to take a tough line against the Soviets and Cubans in Africa have gained the upper hand over factions in the State Department and elsewhere who advocate more moderate actions and rhetoric on African questions.

At one point, he came close to publicly rebuking United Nations Ambassador Andrew Young, who has said that the administration already has sufficient freedom to act in Africa and has described as "ridiculous" any assigning of strategic importance to countries simply because of a Cuban military presence.

Brzezinski said a country like Ethiopia, which Cuba and the Soviet Union aided in a recent conflict with Somalia, is important because of its geographic location in the Horn of Africa. Zaire, he added, is important because of its size and its mineral resources.

"These are the strategic concerns that have to be taken into account," he asserted. "I do not believe that sticking one's head into the sand is the best solution to difficult problems in the world."

But, despite his advocacy of a more activist U.S. role in Africa, Brzezinski was careful to stress the administration's assurances that the United States will not become involved militarily on that continent.

The proper response, he said, "is not by the United States alone, but it is by the international community as a whole, with the United States taking a part in it, perhaps not even the leading part . . ."

Others who should be playing a role, he said, are the African states that do not want a Soviet-Cuban intrusion in their midst and Washington's West European allies. Although Brzezinski did not say so, the question of concerted U.S.-European action in Africa is expected to figure prominently in discussions opening here tomorrow among heads of North Atlantic Treaty Organization nations.

Underscoring the attention that the administration has focused on Africa was the fact that Brzezinski, in his TV interview, was asked far more questions about that subject than about his just completed trip to China.

In respect ot China, he denied that the administration wants to exploit Soviet-Chinese tensions. The purpose of his trip, he said, was "to engage in a comprehensive consultative review" of U.S. and Chinese policies, to reaffirm the U.S. commitment to furthering normal relations and to see whether the present state of those relations can be developed further.