President Carter yesterday put his prestige behind efforts to head off a confrontation with South Africa at the United Nations over Namibia, but his administration was unable to report any immediate progress toward that goal.

The president and his senior foreign policy advisers met with South African Foreign Minister Pik Botha in the White House for a 15-minute discussion of elections in the disputed mandated territory after Botha held a longer meeting with Secretary of State Cyrus R. Vance at the State Department.

Botha flew unexpectedly to Washington Wednesday to arrange the meeting with Vance after talks with the secretary and U.N. Secretary General Kurt Waldheim in New York earlier in the week had ended in what diplomatic sources described as a deadlock.

The five Western members of the Security Council say they fear that the deadlock will lead to calls in the council next week for economic sanctions against South Africa, a key trading partner and investment center for the Western nations.

Speaking after the White House meeting, which the administration had refused to disclose in advance, State Department spokesman Hodding Carter would say only that Vance had "stressed the urgency of South Africa moving rapidly" to break the deadlock.

He refused to characterize the talks in any way. On Monday, after Vance had flown to New York for a hastily scheduled meeting with Botha, the State Department characterized their talks as "thorough and useful."

Vance and Botha reportedly dealt with the Namibia elections dispute in a general way at the Monday talks, and it was later in the week in discussions with Waldheim and representatives of the five Western "contact group" nations that Botha said he was unable to give the Security Council two key assurances the West is seeking.

South Africa has failed to give commitments on a starting date for the arrival of a U.N. peacekeeping force that would supervise elections next year. Pretoria also continues to be ambiguous about the status of the local governing authority that will emerge from unilaterially scheduled elections to be held beginning Monday.

White House and State Department aides were unable to offer any public explanation for the sudden involvement of the president in the diplomatic exercise. The tone and sequence of events as described by Hodding Carter suggested that Vance had arranged the White House meeting for Botha to hear, directly from the president, U.S. concern over the impending showdown on sanctions, but this could not be confirmed officially.

Botha was flying back to South Africa last night from Washington to report to the cabinet, and, depending on the outcome of the cabinet meeting early next week, might be sending further messages to Vance and Waldheim on Namibia, a South African embassy spokesman said.

South Africa was awarded control of Namibia, which is also known as South West Africa, in 1920 under a League of Nations mandate. The United Nations has dclared the mandate terminated, and considers the week-long elections that start Monday under South African control to be illegal.

A. U.N.-sponsored agreement between the Soviet-backed guerrilla forces of the South West African Peoples Orangization (SWAPO) and South Africa for U.N.-supervised elections fell apart in September, when Pretoria withdrew its agreement and scheduled the unilateral voting, which SWAPO is boycotting.