Americans overwhelmingly support the black majority seeking equality in South Africa but are divided about President Reagan's handling of U.S. relations with South Africa, according to a new Washington Post-ABC News poll.

The poll, conducted Sept. 19-23, followed Reagan's decision to impose limited economic sanctions against South Africa in an effort to avoid stronger sanctions pending in Congess.

A year-long cycle of violence in South Africa dealing with its policy of apartheid, or rigid racial segregation, has claimed about 700 lives and intensified demands in the United States for punitive measures against Pretoria.

Reagan recently promised to take a more "activist" approach to his policy of "constructive engagement" toward South Africa, which relies on persuasion rather than coercion in seeking an end to apartheid.

Asked whether their sympathies are more with the black majority in South Africa or the white government, 64 percent of those questioned said the black population, 13 percent said the white government, 5 percent said each equally, 4 percent said neither and 14 percent expressed no opinion.

These findings are similar to those reported by the Gallup Poll in August.

The new Post-ABC poll showed that 48 percent think that Reagan's sympathies are with the white-minority government, while 20 percent said the president is more sympathetic to the black population, 6 percent said each equally, 3 percent said neither and 23 percent offered no opinion.

Those polled were also divided when asked to weigh additional freedoms for blacks against the value of South Africa as a stable western ally.

Forty-seven percent said giving South Africa's blacks more freedom is more important even if that weakens the country's stability or loosens ties to the West.

Thirty-nine percent said keeping South Africa as a stable ally is more important even if it means delay in giving blacks additional freedom. The rest said they did not know or had no opinion.

Asked about Reagan's handling of relations with South Africa, 44 percent said they approved, and 43 percent said they disapproved.

Questioned about U.S. pressure on South Africa to reform apartheid, 16 percent said there is too much pressure, 39 percent said too little, 31 percent about the right amount, and 14 percent had no opinion or did not know.

The poll also showed that Americans under age 45 are more strongly in favor of additional pressure on South Africa than those older. A substantial number of Democrats and Republicans favored more pressure, although sentiment among Democrats appeared stronger.

The survey also showed Reagan's overall approval rating at 62 percent, down from 65 percent in a July poll.

The nationwide telephone survey consisted of interviews with 1,512 people and has a theoretical margin of sampling error of plus or minus 3 percentage points.