Ethiopia announced yesterday a major offensive in Eritrea and claimed support by the Soviet Union, Cuba and other Communist nations to crush the 16-year-old secessionist rebellion in the province bordering the Red Sea.

Eritrean guerrilla spokesmen called the long-anticipated assault, "the largest offensive" ever launched by the central government in Addis Ababa, and said it registered a quick success as 20,000 Ethiopian troops broke out of a guerrilla encirclement. Asmara, the capital of Ethiopia's Eritrean province, has been under seige since February 1975.

"However, it is not correct to say that the siege of Asmara has been broken completely," said a Beirut spokesman for one of the main groups fighting for Eritrean independence - the Eritrean Liberation Front-Revolutionary Council.

The spokesman said about half of the Ethiopian garrison in Asmara, estimated at 40,000 men in its entirety, pierced the guerrilla lines in one sector and he said heavy fighting was raging around Adi Teklai, about six miles west of Asmara.

Ethiopian fighter bombers, the guerrilla spokesman said, began pounding villages Monday along the Red Sea coast between Massawa, the major port, and Assab, 300 miles south. Guerrillas have claimed control of all but five cities in Eritrea and more than 90 percent of the countryside.

The leader of Ethiopia's military government, Lt. Col. Mengistu Haile Mariam, declared in a speech read in his name over Radio Ethiopia yesterday:

"In the friends' camp we have the USSR, Cuba, the South Yemen, East Germany and other genuine socialist countries and progressives that have supported us through their actual deeds.

"The genuine progressive comrades whom we have mentioned above are living with us, dying with us, and fighting with us, standing by the side of the broad masses of Ethiopia and their revolution after having traveled several thousand miles . . . In the enemy camp, international imperialism and all its puppets have risen up against us."

Carter administration officials said yesterday that they believe Mengistu's reference to Soviets, Cubans and others fighting and dying alongside Ethiopian troops in Eritrea right now is probably "rhetorical" rather than factual - but they can only speculate about what is actually happening.

There are an estimated 15,000 to 17,000 Cuban troops in Ethiopia, left there since the Ogaden border war between Ethiopia and Somalia. A major question dangling for months has been whether Mengistu could induce Cuban President Fidel Castro to commit these troops to the wars in Eritrea.

American Analysts are convinced that Cuban and Soviet military advisers have supplied strategic advice to Ethiopia for the Eritrean conflict. In addition, a few weeks ago, several Cuban pilots were reported flying combat missions in Eritrea.

State Department spokesman Hodding Carter said yesterday that the United States has no immediate knowledge of the extent of fighting in Eritrea but "it does appear from statements . . . that major fighting is now in progress."

President Carter has said that the use of Cuban troops and Soviet military advisers in Ethiopia during the conflict with Somalia represented an "ominous" development. Reiterating that theme yesterday, the State Department's Carter said, "It is contrary to the African principle that regional problems should be solved by the Africans themselves."

Referring to Eritrea, spokesman Carter said, "We deplore the continuing, serious bloodshed. We are prepared to accept any solution mutually agreed to by the Ethiopians and the Eritreans."

But the spokesman bluntly conceded that "there are some fairly limited possibilities" about what the United States is prepared to do.

Secretary of State Cyrus Vance last month in Moscow urged the Soviet Union, which has provided an estimated $1 billion in military supplies to Ethiopia during the past year, to exercise restraint in its African ventures. There was no indication that Vance received any comfort on this request to Soviet President Leonid Brezhnev.

Soviet Foreign Minister Andrei Gromyko is expected in Washington within a week to continue negotiations in the nuclear strategic arms limitation talks (SALT).

Former Secretary of State Henry Kissinger, in a NBC-TV commentary Monday night, said that if Cubans turn out to be involved in the Eritrean conflict, "we must hold the Soviet Union responsbile. Ultimately they placed the Cubans there . . . I think the Soviet Union must be told that it has to choose between negotiations with us or an imperial policy in Africa. It cannot have both."

Kissinger, like the Carter administration, generally used to maintain that the nuclear arms control negotiations, the crux of U.S.-Soviet detente, are too vital to be linked to Soviet actions in Africa. Kissinger, Monday night, said "Up to this point I have agreed with the administration that SALT should not be lined with what has happened so far."

"But in light of what has happened recently in Afghanistan - where the Communists have taken over." Kissinger said, and in light of "what now appears to be occurring in Zaire" (referring to the invasion of Shaba Province by forces based in Marxist-ruled Angola), ". . . I think we ought to review the whole negotiations - all of our negotiations with the Soviets."

State Department spokesman Carter, however, said yesterday, in answer to questions: "Are we going to negotiate on the SALT agreement? We're going to negotiate on the SALT agreement. Are we going to, in effect, pretend that this (Soviet-Cuban intervention in Africa) isn't going on? No."

What the United States can do, he said, is to try, through diplomatic channels and other means, to convince other nations that "we don't think the involvement of foreign forces is appropriate" in Africa.

Paradoxically, President Carter today will be receiving Zambian President Kenneth Kaunda on a two-day state visit in which Kaunda will be warning that it may become necessary for Africa's black nationalists to turn in desperation to Cuba's troops to help bring black majority rule to Rhodesia.

Some of the guerrilla forces fighting for black control of Rhodesia are based in Zambia, where there are some Cuban military advisers now.

Kaunda denied recent reports that he wants Cuban troops to enter the struggle for Rhodesia.

A senior State Department official said yesterday that Kaunda's position is that "he may be forced to call for help where he can get it," and that the possible call on Cuban forces represents "an expression of a fear" on Kaunda's part, rather than a desire. Kaunda fears, the official said, that "if he really needs help, the West may . . . not come to his assistance."