Rhodesia's exiled black nationalist leaders, Joshua Nkomo and Robert Mugabe, today rejected any further talks on the Anglo-American peace plan until Britain abandons what they called a "double-faced outlook" toward negotiations for a settlement of the 12-year-old Rhodesia dispute.

Accusing both London and Washington of a "somersault" in their attitude toward Rhodesian Prime Minister Ian Smith, the two leaders said they found "no cause to continue discussions" until British Foreign Secretary David Owen "recommits himself to his original undertaking" of working for the removal of Smith and the dismantling of his armed forces.

The two co-leaders of the Patriotic Front, the main umbralla guerilla organization, had been invited to go to London next Tuesday for a new round of talks with Owen on the Anglo-American proposals. These proposals are aimed at achieving a peaceful transition to black majority rule in the breakaway British colony before the end of next year.

Their decision to boycott the London meeting is the latest in a series of serious setbacks over the past two weeks to the Western initiative in Rhodesia that now seems to be heading rapidly toward failure.

While their joint press statement did not exclude later discussions on the British-American plan, Mugabe and Nkomo made it clear they would not participate so long as British and American officials appeared to be faltering in their determination to oust Smith and place a black majority government in power.

Two weeks ago today, Smith announced his rejection of the latest Anglo-American plan and said he was going ahead with his own "internal solution" involving more moderate black nationalist leaders living inside Rhodesia. At the same time, he announced his conditional acceptance of the principle of majority rule based on adult suffrage as the basis for a settlement.

Britain immediately hinted that it might be prepared to accept this approach by Smith, provided elections these outside Rhodesia, were given the opportunity to participate.

Smith's announcement came just as Rhodesia launched its biggest incursion into the eastern border region of this country in an attempt to shatter the main guerrilla force. As many as 3,000 guerrillas and civilians may have been killed or wounded and their main headquarters in Mozambique was largely destroyed.

Then on Tuesday, Zambian President Kenneth Kaunda announced he was withdrawing his support from the British-American plan, thereby splitting the five "front-line" African states whose support and unity have been regarded as indispendable for obtaining a negotiated settlement.

At their press conference after four days of talks between the Front's two rival factions, Nkomo and Mugabe accused Owen of abandoning his own proposals and adopting a "welcoming posture," toward Smith's initiative. They also accused U.S. Secretary of State Cyrus Vance of joining Owen in a "somersault toward Smith."

Prior to issuing their joint declaration on the London meeting, it had appeared that the two leaders were taking different positions on several key issues relating to the British-American proposals.