Secretary of State Cyrus R. Vance and British Foreign Secretary David Owen agreed yesterday that Rhodesia's plan for black majority rule must be greatly improved to avert black-black civil war across southern Africa.

The ultimate danger of greater Soviet-Cuban military involvement in Africa is dangling over the American-British-African discussions, here and at the United Nations.

Amercian and British strategy is to straddle the present dispute, in an attempt to encourage a compromise between the African nationalists inside Rhodesia who last week signed a peace plan with Rhodesian Prime Minister Ian Smith, and the Africans outside Rhodesia who denounce the plan as "a sellout" to the whites.

"A lot of the credibility of our entire African policy turns on how we behave in this situation," said a senior U.S. official.

President Carter can be personally involved in the outcome. At the end of this month, Carter plans to visit Nigeria, one of the African nations leading the challenge to the deal struck between Smith, Bishop Abel Muzorewa and two other black nationlist leaders inside Rhodesia.

Vance talked yesterday morning with Muzorewa andd then with Britain's Owen. During the day of discussions, Vance and Owen also met for about 20 minutes with President Carter at the White House, to hear his urgings for pursuit of a peaceful solution of the clash. There is heavy political pressure inside Britain on Owen from white conservatives and moderates to accept the so-called "internal solution." Amercian strategists, so far experiencing less domestic political outcry, are taking a lead in trying to bring the opposing Africans nationalists together. But U.S. planners also are concerned about a political backfire if no compromise is reached.

After his first round of talks yesterday with Owen, Vance said of Britain and the United States: "We've been going in step on this for a long time, and still are."

Muzorewa said he was "very encouraged" by his meeting with Vance, but Vance and Owen afterward took a position far from the terms Muzorewa accepted.

Vance said that while the Salisbury accord, as it is known, "was a significant step" toward black majority rule in Rhodesia, "a great deal remains unclear about what is involved in that proposal . . ."

He and Owen are agreed, Vance said, that "the yardstick" against which they will measure "any proposal remains the Anglo-American plan" to which they are committed.

The agreement signed in Salisbury last week, to bring majority rule for the nation of 6.7 million blacks and 263,000 whites, would make Smith and three black ministers the central authority until elections produce a new government on Dec.31.

Under the Anglo-American plan, among other things, Smith would have lost power at the outset of the transition, with Britain, which formerly ruled Rhodesia, resuming control until the formation of a majority government.

Vance said the Salisbury plan does provide for such improvements as universal suffrage and independent judiciary, contained in the Anglo-American proposal.

But the key "transitional arrangements" for shifting to black majority rule are still unclear in the Salisbury plan, Vance said. Also missing from it, Owen added, are provisions for "a cease-fire" to end the guerrilla warfare between Rhodesia and the black nationalist Patriotic Front, led by Joshua Nkomo and Robert Mugabe, from bases iN Mozambique and Zambia.

Owen said that although there are "some significant similarities" between the two plans, "there are quite so many differences."

Asked if the Salisbury plan is constructive enough to warrant removing the economic sanctions which the United Nations voted against Rhodesia after Smith'a government unilaterally declared independence from Britain in 1965, Vance replied, "No."

Vance and Owen both said they have not decided if they will participate in the U.N. Security Council debate now under way, called on request of African nations to condemn the Salisbury agreement.

This debate will also test the resourcefulness and credibility of American Ambassador Andrew Young, the Carter administration's "point man" on African policy. In search of a compromise formula, Young had breakfast Tuesday with Nkomo, lunch yesterday with Mugabe, and is to meet Muzorewa at breakfast today.

An authoritiative administration official said privately that the United States is secretly siding with the white minority regime in Rhodesia.

"The Africans simply don't trust us," said this source, "and Andy and the President have brought us the benefit of the doubt."

If there is no road left open to the Patriotic Front but escalating the guerrilla war against Rhodesia, U.S. planners say, Nkomo and Mugabe are bound to turn - as they have warned - to the Soviet Union and Cuba for reinforcing troops and supplies.

With up to 20,000 Cuban troops now in Angola, and 11,000 in Ethiopia along with Soviet advisers and military supplies, there will be a strong Soviet-Cuban inclination to make a new commitment in southern Africa "where the stakes are much greater," and administration official said. Cubans for some time been training Rhodesian guerrillas at bases in Zambia and Mozambique.

At the United Nations on Monday, Ambassador Salim A. Salim of Tanzania, one of the "front-line" states supporting the guerrillas, said the African nations will be closely watching to see if the United States and Britain "abandon their own proposals" and support Rhodesia's attempt "to bamboozle world public opinion by appearing to accept . . . majority rule."

Bishop Muzorewa, however, a dimunitive but highly vocal personality, yesterday vigorously defended what he and fellow nationalists Ndabaningi Sithole and Jeremiah Chirau negotiated with Smith.