Western efforts to get South Africa to agree to a new plan for independence for Namibia reached "a difficult stage" last night, U.S. and British spokesmen announced as the two sides recessed negotiations.

The spokesmen declined to give details of the snags that developed in the second day of talks that are viewed as crucial both for South African ties to the five nations negotiating on behalf of the United Nations here, and for the Carter administration's diplomatic credibility in Black Africa.

But the central issue dividing the Western group and Prime Minister P. W. Botha's Cabinet was reliably reported to be the status of elections that South Africa plans to hold in the disputed territory in December. South Africa announced the elections last month after withdrawing from an agreement with the United Nations for elections, tentatively set for the spring.

Earlier in the day, the two sides reportedly had made progress on other disputed issues and had agreed to discuss a compromise plan under which the South Africans could go ahead with the December elections but only as a preliminary ballot for a binding U.N. supervised election next year.

It was after this plan reportedly went to the South African Cabinet that the "difficulties" were publicly announced. Diplomatic observers did not exclude the possibility of last-minute maneuvering aimed at public opinion by both sides before a compromise is reached.

State Department spokesman Hodding Carter III declined to give any details of the talks or to comment on the reported election proposal. Carter said that the five nation group was waiting for an unspecified message from the South Africans before deciding whether there would be any more meetings.

The talks had been scheduled originally to end yesterday so Secretary of State Cyrus Vance could leave early today for Geneva and begin preparing to go to Moscow on Saturday for the final round of strategic arms limitation talks with the Soviet Union.

Joining Vance in trying to persuade the South Africans are the foreign ministers of Britain, Canada and West Germany and the deputy foreign minister of France. If South Africa does not accept the plan it faces U.N. censure and a possible mvoe for economic sanctions.

South Africa has ruled the mineral-rich, sparsely inhabited territory, also known as Southwest Africa, since 1920. After a decade of resisting both U.N. pressur to get out and a low-level guerrilla insurgency. South Africa agreed in April to a plan that would have brought U.N. peacekeeping forces into Namibia to oversee elections open to the guerrillas of the Southwest African People's Organization. But South Africa withdrew from the agreement shortly after SWAPO accepted it.

One potential signal that yesterday's discussions had moved onto the disputed elections came when John Vaill, a top legal official in the South African-appointed local administration in Southwest Africa, suddenly left Pretoria for the provincial capital of Windhoek. He reportedly carried a message for Dirk Mudge, the head of the Democratic Turnhalle Alliance, the group that South Africa apparently expects to win the December elections.

The South Africans need Mudge's acquiescence to an agreement with the West that would affect the December vote. According to one report. Botha would also like Mudge to be responsible for giving the five nations the commitment to accept the previously agreed U.N. plan after the first elections are out of the way.

South Africa fears that the Turnhalle group, would lose ground rapidly to SWAPO if a U.N. buffer force is introduced and elections delayed. This helped trigger the decision to insist on elections before the end of the year, diplomatic sources report.

A blackout continued on the contents of a letter from President Carter that Vance handed to Prime Minister Botha Monday in a private meeting. The format of the talks suggested that the letter concerned southern Africa in genral rather than the specific question of Namibia.