President Carter accused Cuba yesterday of training and equipping the Katangan rebels who invaded Zaire and said Cuba must share responsibility for the bloody attack.

Carter's charges, the harshest and most explicit that his administration has directed against Cuba, were made at a press conference in Chicago.

His accusations, made in an opening statement, ran counter to assertions by the government of President Fidel Castro that Cuban played no role in training, equipping or cooperating with the Katangan invasion forces.

Informed sources said the President's statement was based on intelligence received by the Administration within the last couple of days. The sources added that Carter's decision to speak out bluntly about the Cuban role in the Katangan conflict was made yesterday morning, just before the start of his two-day political trip.

At the press conference, Carter bore down heavily on Soviet and Cuban military involvement in African conflicts and the question of whether the United States is able to play an countering role.

He rejected suggestions that Washington should link a new strategic arms limitation talks (SALT) agreement with the Soviet Union to demands for Soviet restraint in Africa. But he warned that continued aggressive Soviet behavior on the continent would make it difficult to win approval for a SALT agreement from the American people and Congress.

Carter also reiterated administration complaints of recent days that Congress has tied an effective U.S. response in Africa and other parts of the Third World.

The president warned that he will oppose any new congressional efforts to put restrictions on the use of aid, loans and other peaceful means of excercising U.S. influence in developing countries.

His harshest words, though, were directed at Cuba. He said: "We believe that Cuba had known of the Katangan plans to invade and obviously did nothing to restrain them from crossing the border. We also know that the Cubans have played a key role in training and equipping the Katangans who attacked."

Cuban officials have been denying such charges ever since the fighting in Katanga began almost two weeks ago. At one point, Castro personally told the head of the U.S. interests section in Havana that there were no Cubans with the invading rebels.

Last Saturday, the Cubans foreign ministry issued a statement saying: "The Cuban government categorically reiterates that there do not exist now, nor have there ever existed, ties of military cooperation between Cuba and these forces; that Cuba has not furnished any military equipment to them; that Cuba has not trained them or had any part in their actions and that there are no Cuban troops or technicians in Zaire."

In his statment, Carter also criticized the Marxist government of Angola, saying it must bear a heavy responsibility for the attack which was launched from its territory."

He said the U.S. role in the international operation to rescue persons trapped by the fighting "has virtually come to an end" and added: "Our transport aircraft will be returning to their bases within the next few days."

When asked whether the United States should inject the Africa situation into the SALT negotiations, the president replied, "I think a SALT agreement is so important to our country and the safety of the entire world that we should not permit any impediment to come between us and the reaching of a successful agreement."

However, Carter added, he had no doubt that Soviet actions in Africa, plus those of its ally Cuba, would affect the attitudes of the American people and Congress, which must approve any SALT agreement.

A similar note was sounded yesterday by Secretary of State Cyrus R. Vance in a New York television interview before he began a private meeting there with Soviet Foreign Minister Andrei Gromyko.

Vance underscored that Soviet-Cuban actions in Africa would be an important issue in the discussions and said: "The only way to deal with these problems is to get them out on the table and talk shoulder-to-shoulder very straight."

Senior administration officials said yesterday the White House has instructed Vance to give Gromyko a stern lecture on U.S. concern about the African situation.

According to these officials, the Soviet and U.S. governments have been discussing the idea of a summit meeting between Carter and Leonid I. Brezhnev, first secretary of the Soviet Communist Party, in July, somewhere in the United States but outside of Washington. The recent increase in tensions now makes it possible, perhaps likely, that the summit will be delayed, the officials said.

In addition, the sources added, administration strategists are discussing prolonging the SALT negotiations, postponing a final effort to complete a new accord until late this year.

On the question of whether a post-Vietnam reaction has caused Congress to put too many restrictions on the president's use of foreign aid, Carter complained, "I can't compete at all, even peacefully, in Africa."

"We do not want to send our military forces into Africa to meet the challenge of Soviet and Cuban intrusion . . . I have no intention of getting involved in any conflict," Carter said.

But, he added, Congress has had "an increasing inclination" to restrict aid to certain countries where it is important for the United States to have influence.

"For instance," Carter said, "last year the House tried to put restrictions on any aid to any country which produced sugar because our own country produces sugar. That might force countries who desperately desire our help to turn to the Soviet Union for it."

He cited three African countries - Uganda, Tanzania and Mozambique - that have been singled out by Congress for cutoffs or restrictions in aid. "If we are prevented from giving them any aid, even food, then my hands are tied," Carter asserted.

None of these countries have been involved in recent African disputes or fighting where the administration says there has been a Soviet or Cuban presence. In addition to Zaire, the administration's concern has been focused mainly on Soviet-Cuban aid to Ethiopia, which recently fought a war with somalia, and to rebels operating against the transitional government in Rhodesia.

In talking about restrictive legislation, Carter cited the Clark amendment, named for its sponsor, Sen. Dick Clark (D-Iowa). It forbids any direct or indirect U.S. aid to Angola without expressed congressional authorization.

However, Carter said, he is not seeking the repeal of the Clark amendment or any other legislative restrictions at this time. Instead, he added, the administration will wait for the results of a study being made by the State Department before consulting further with Congress.

The president was not asked yesterday about the plan that Adm. Stansfield Turner, director of the Central Intelligence Agency, showed to Clark earlier this month, out-lining a proposal for U.S. assistance to rebels fighting the Marxist regime in Angola.

Clark said last night he was reassured by Carter's press conference statements and was pleased that the administration now seems to be focusing on an easing of restrictions on economic rather than military aid. Clark also said he was "increasingly confident that the plan shown to me by Adm. Turner did not originate with the president."