In a dramatic reversal, Rhodesian Prime Minister Ian Smith announced today that he was inviting Britain and the United Nations to send their designated representatives to Salisbury for further talks on the British-American plan for settlement of the Rhodesia dispute.

The immediate assessment of Smith's surprise move was that he was slowly bowing to mounting pressure from South Africa and other countries to yield to the British-American plan for bringing about black majority rule.

Since Rhodesia's unilateral declaration of independence from Britain 12 years ago, the idea of returning power to Britain - virtually the first step in the Anglo-American plan - has been strongly opposed by Smith and his white minority government.

A Rhodesian government spokesman was careful to state that the invitation extended by Smith did not imply acceptance of the peace proposal. Rhodesia, a spokesman said, was interested in further talks now mainly to secure a cease-fire in the war with black nationalist guerrillas.

In their interpretation of Smith's invitation, observers here felt that Smith was also playing for time, as he so often has in the past, in the hope that some new development will spare his government from surrendering power. In addition, he appears to want to avoid being blamed for the failure of the plan and to be calculating that the African nationalists will refuse it anyway.

Announcement of Smith's invitation was apparently timed for today's meeting of the U.N. Security Council at which Britain and the United States formally requested the appointment of a special U.N. representative to deal with the transfer of power in Rhodesia.

The British have already named Field Marshal Lord Carver to be their resident commissioner in charge of the transitional administration between the white and black governments.

The naming of a U.N. representative would represent the first step in the involvement of the world body in backing the British-run transition administration. The British and Americans want the Security Council to establish a peace-Keeping force to support the British commissioner in his task.

The Anglo-American plan calls for Smith to "surrender" power peace-fully to the British and provides for transition to black majority rule by the end of 1978 with free elections based on the principle of one-man, one-vote.

Smith's initial reaction to the seven-point plan was that it was "ill-conceived" and most of its key provisions "insane" and "crazy". The proposals were outlined to him Sept. 1 by British Foreign Secretary David Owen and the U.S. Ambassador to the United Nations. Andrew Young.

He specifically criticized the role proposed for the British resident commissioner and the idea of a U.N. peace-keeping force unless it was under Rhodesian army authority. He also rejected proposal for the "liberation forces" to form the basis of a new national army.

The Rhodesian signal to the British and American governments, as well as to the United Nations, follows a number of developments that have undoubtedly given Smith second thoughts about what strategy to use to circumvent the plan through his so-called "internal solution" negotiated with the most moderate African leaders in Rhodesla.

First, the two main African leaders he has been courting, Bishop Abel Muzorewa and Rev. Ndabiningi Sithole, have both indicated they support the Anglo-American plan and oppose hid internal solution.

Secondly, Smith met with South African Prime Minister John Vorster after publication of the plan and was reportedly told that South Africa wants an internationally acceptable solution such as probably only the Anglo-American proposals would provide.

While Vorster has strenuously avoided dictating to Smith, he has also been pointing out the "realties" of the Rhodesian government's deteriorating situation, according to South African sources.

Thirdly, leaders of the five African states most involved in the dispute met in the Mozambican capital, Maputo, last weekend and approved the Anglo-American proposals as a "basis for further negotiations" despite what they called a "lot of negative points" and unanswered questions in it. By so doing, they placed the burden for any failure of the plan on Smith.

Finally, Smith and his thinly stretched army are facing the beginning of a new rainy season, a time traditionally chisen by guerrillas to step up their attacks.

One of the firs tasks of the British commissioner and the U.N. representative will be to arrange for a cease-fire. If this were achieved, the Rhodesian army and government would be spared the expected offensive.

Officially, the Anglo-American plan simply states that the U.N. secretary general "will be invited to appiont a representative th enter into discussions, before the transition period, with the British resident commissioner-designate and with all the parties with a view to establiching in detail the respective roles of all forces in Rhodesia."

Since both the Patriotic Front, the main black Nationalst group, and Smith have rejected a U.N. peace-keeping force and an all powerful resident commissioner and both are seeking to dominate the transition process, it would appear th British and U.N. Special representatives have a difficult task ahead of them in trying to establish an interim government independent of all the contending partics and to arrange for elections.