The United States and Nigeria reached a major diplomatic reconciliation today, with the military government here welcoming an active American role in negotiating an end to white rule in southern Africa.

The new mood of cooperation emerged from a three-hour meeting between Andrew Young, U.S. ambassador to the United Nations, and Lt. Gen. Olusegun Obasanjo, Nigerian head of state. It contrasted with Nigeria's hostility toward former Secretary of State Henry A. Kissinger's efforts to negotiate change in Rhodesia South Africa and Namibia (Southwest Africa).

U.S. Ambassador to Nigeria Donald Easrum summed up the meeting at Obasanjo's military headquarters by stating: "It was the most interesting and perhaps the most important conversation of this nature I've had in 23 years in the Foreign Service."

Obasanjo, who agreed to a rare joint news conference to mark the reconciliation, said in reply to a question about the state of relations now between Nigeria and the United States: "I cannot describe the relationship as strained by any stretch of the imagination."

He added, "We agreed on what should be done, our course of action, methods of approach and our tactics." Neither side spelled out just what Concrete measures they had in mind.

The clearest diplomatic suggestion to emerge from Young's week-old African mission involved a possible meeting of all parties - except South Africa and Rhodesia - to help put the abandoned Geneva conference back on the rails.

Young said the United States, Britain, Nigeria, Zaire and the so-called frontline states of Angola, Botswana, Mozambique, Tanzania and Zambia could participate as well as all the rival Rhodesian nationalist groups.

Young said that if such a conference could work out a united position - principally by ironing out differences among the rival nationalist leaders - it would be "very hard for [Rhodesian prime minister Ian Smith and (South African Prime Minister John] Vorster to buck."

Last month Smith withdrew from the moribund Geneva talks by turning down British negotiator Ivor Richard's suggestion for a solution.

Young said he would discuss the new proposal with the British government when he flies to London Friday before returning to the United States. He stressed that both President Carter and Secretary of State Cyrus R. Vance would have to consider the proposal and that "I was very careful not to commit us to anything."

Gen. Obasanjo made clear his desire for a new departure in relations with the United States. Nigeria, black Africa's richest and most populous state, has become the United States' second biggest source of foreign oil after Saudi Arabia.

He described his meeting with Young as a "refreshing opportunity to be able to consider together and very intimately and frankly what should be the areas of cooperation between Nigeria and the United States, not only in terms of our two countries but in terms of the interests of the continent of Africa and the world at large."

Nigeria was at odds with the Ford administration over Angola, backing President Agostinho Neto's leftist regime. This was to the displeasure of the United States, which opposed the presence of Soviet - supplied Cuban troops in the former Portugese colony.

Obasanjo's government thrice refused the efforts of Kissinger to visit Lagos at the time of his mission to Africa last spring. It was then that the United States announced on active role in southern African problems.

Today, Obasanjo said that "it was not until the United States stepped in and brought the necessary pressures to bear that Smith accepted the principle of majority rule."

Using the nationalist name for Rhodesia. Obasanjo said, "it stands to reason that to achieve any success in solving the problems to Zimbabwe, the United States has to be involved."

Obasanjo said he favored economic pressures for change in South Africa, adding that he and Young "did discuss the appropriate pressure the new administration in the United States can bring to bear."

Young, however, told reporters he had informed a "very understanding" Obasanjo of the administration's reluctance to impose "blanket sanctions" against South Africa to force black-majority rule.

Young drew on his experience in the civil rights movement in the American south to explain how "selective" punitive economic measures could encourage recalcitrant businesses to make desired changes.

Obasanjo was reported to have expressed concern that the United States under Kissinger had already played into South African hands by withdrawing pressure for a Southwest Africa settlement in return for Vorster's now evaporated promises to pressure Smith into an orderly Rhodesian solution.

The Nigerian leader was also reported to have warned that any settlement which did not take into account the Southwest African People's Organization - now excluded from negotiations by South Africa - would mean continuing civil strife there.

Asked if he had been surprised at the new aura of good bilateral feelings, Young replied. "Yes, in a way, because Nigeria had been represented as the big, boy of Africa and traditionally anti-American, I frankly expected to be received with a short lecture - if not a long one - on the past sins of the United States towards Nigeria."

Here, as in east Africa, Young said he had stressed the need to move cautiously and said the African leaders he met understood that "we are looking for a breathing space to give the Carter administration a chance to get its act together."

Despite what Young described as the "very warm and cordial" attitude, Obasanjo cautioned that unless the Carter administration made good on its promises, relations with the United States "could slip back even further than they were before."

But with Nigeria in mind, Young said, "with governments that were supposed to be the most militant I've been able to be the most conservative and get away with it."

[In Addis Ababa, Ethiopia, the secretary general of the Organization of African Unity welcomed Young's visit to Africa as a "healthy sign." Eteki Mboumoua, the OAS leader, also urged the creation of a joint African military force to help defend African countries against mercenary attacks.]