Negotiations on removing South African troops from Angola have reached "an extremely delicate phase" in which both parties have agreed in principle to complete the process as soon as possible, a senior State Department official said yesterday.

Angola has agreed that, when that is accomplished, withdrawal of Cuban troops from Angolan territory will be "a part of the package" of overall peace in the region, the official said.

"We are at the beginning of what could become the end game of an overall settlement," the official added.

Briefing reporters on condition that he not be named, the official said that meetings in the next few days could prove decisive on both issues and that the United States has been playing "a key mediator role."

Ridding Angola of the estimated 25,000 Cuban troops there has been the focus of the Reagan administration's Africa policy. It has also been the center of three years of diplomatic effort by Assistant Secretary of State Chester A. Crocker, who returned here yesterday from two days of talks with South African diplomats in the Cape Verde Islands.

The official said the South Africans have "undertaken to study and respond" by late this month to new proposals brought to them by Crocker from Angolan President Jose Eduardo dos Santos.

The proposals, which dos Santos first outlined in an Oct. 14 interview with The Washington Post, link Cuban withdrawal from Angola to South African withdrawal from Namibia, which lies between South Africa and Angola.

"It clearly means Cubans would be departing from Angola in the context of a Namibia settlement, and that is not a position we have been in for the past three years," the official said.

All further progress, however, may hinge on departure from southern Angola of the last 2,000 of an estimated 20,000 South African troops who invaded Angola late last year, ostensibly to chase rebels trying to overthrow the Namibian government.

South Africa agreed in February to withdraw troops from Angola in five stages ending March 30, but it never completed the final stage. South African officials said they were awaiting further proposals from Angola on Namibia and the Cuban troops.

The State Department official said there is "will and desire on the part of both the Angolans and the South Africans to complete the withdrawal process as soon as possible."

One achievement, he said, was an understanding that rebels using Angola as a base from which to attack the Namibian government will not move into any Angolan area vacated by South African troops.

However, he said, no major breakthrough has occurred, and "arduous work" remains to be done. "We are in an extremely delicate phase of a very complex negotiation," he said. He refused to predict how long the process might take.

The official added in response to questions that, during the Cape Verde meeting, Crocker had criticized South Africa's apartheid policies. The meeting included South African Foreign Minister R.F. (Pik) Botha.

"We have made clear repeatedly . . . our concern about violence and our belief that there needs to be a dialogue within South Africa," the official said. "That is the way you solve internal problems there."