The Reagan administration yesterday announced a policy of "constructive engagement" with South Africa after two days of talks at which the United States sought, but did not fully achieve, a meeting of minds about the touch problem of Namibia.

A senior State Department official who participated in the talks said South African Foreign Minister Roelof (Pik) Botha was informed that a U.S. policy of "constructive engagement" rather than one of "confrontation" has been chosen as the best way to bring progress.

In a background briefing for reporters, the State Department official said the new guideline "represents above all the reality that there is a limit on the U.S. capacity to use negative pressure to achieve positive results in South Africa."

Instead of negative pressure, the administration approach is to "positively support that which one wishes to see, both by word and deed," the official said. Reporters were given no details of impending changes in the South African relationships, but were told instead that tangible changes are still under discussion.

President Reagan has labeld South Africa's racial policy of apartheid as "repugnant," but there has been no public drive by the new U.S. administration to demand reforms. The State Department briefer said the administration expressed "at the very highest level of government" -- presumably referring to Reagan's meeting with Botha Friday -- its concern about South African racial policies.

Regarding Namibia, the Reagan administration insisted that the future of the thinly populated mineral-rich area, long under South African control, must be determined by "an internationally recognized settlement," according to the briefing. Secretary of State Alexander M. Haig Jr. made it clear to Botha, according to the official account, that Washington needs to know officially and promptly whether or not Pretoria will cooperate in these ongoing international efforts.

Although Botha spoke publicly Thursday of "a very real possibility" of South African cooperation, he was not authorized to make a definitive statement about cooperation in the negotiating effort of the United States, Britain, Canada, France and West Germany, known as the Western five or "contact group" on Namibia. It is uncertain whether a definitive South African statement of its position will be received from Pretoria before "contact group" officials convene here next Thursday.

Even without South Africa's official reply on the negotitations, Washington and Pretoria appear to be at loggerheads on the means of policing a transition to an independent Namibia.

The South African foreign minister reportedly took the position in the talks with Haig and a senior State Department official who took part, Assistant Secretary of State-designate Chester A. Crocker, that a United Nations military force is no longer acceptable to internal Namibian parties or to South Africa for such a police role.

Previously all parties had agreed that UNTAG (United Nations Transitional Assitance Group), a multinational force of about 7,500 men, would monitor a civil war cease-fire, election and transition.

While acknowledging that Botha expressed "reservations" and "concern" about the U.N. military force, the State Department briefing described UNTAG as "a central element" in the internationally approved framework, U.N. Security Council Resolution 435. Botha was told, according to this account, that eliminating UNTAG from this plan "would be difficult."

South African sources said Crocker had been informed during his trip to Pretoria last month that UNTAG can no longer be accepted as part of the plans for a negotiated transition, and that other nations in the "contact group" had also been given such notice.

In view of this, the South African sources said, it was difficult to understand expressions of U.S. anxiety about Pretoria's position.