President Reagan's personal appeal to South African President Pieter W. Botha last Friday to show restraint on the 10th anniversary of the Soweto uprising was privately rejected by Botha, according to administration officials.

Reagan's appeal was conveyed by U.S. Ambassador Herman W. Nickel. The president was critical of Botha's imposition of a nationwide state of emergency Thursday and the detention of hundreds of activists in an effort to crush dissent.

According to an informed official, Botha was "very rigid" and unresponsive to Reagan's appeal when it was presented by Nickel. The official said the South African appeared to be defiant and obstinate.

Reagan, in a statement issued here that closely paralleled his private appeal to Botha, said that the anniversary of the riots in Soweto had become "a symbol of black aspirations for freedom, equal rights and full political participation."

The president said the United States was calling on "all parties to exercise maximum restraint in searching for solutions to South Africa's severe political crisis."

Reagan also warned that "violence by those who enforce apartheid and by those opposed to it has become so common that South Africa risks becoming a continuing tragedy."

"The American people feel strongly that permitting nonviolent meetings is the hallmark of civilized governments and in the best tradition of the Western democracies," he said.

Both Friday and yesterday, the White House expressed opposition to further economic sanctions against Pretoria as a signal of U.S. displeasure with the crackdown. Reagan said Friday that sanctions would hurt those blacks the United States is seeking to help.

Reagan resisted imposing sanctions against Pretoria last fall, but later agreed to limited sanctions in order to head off more severe ones pending in Congress. The administration is under new pressure in Congress to take such action.

The president also praised the Botha government Friday for its efforts to revoke some aspects of apartheid.

Despite the administration's public posture vis-a-vis South Africa, officials at the State Department, which has been pressing South Africa to open talks with the opposition African National Congress, apparently will not meet with ANC Secretary-General Alfred Nzo, who is visiting here.

Nzo said yesterday that he had asked to see State Department officials but received "no response." "We are ready to talk to them, if they are willing," he said in an interview with editors and reporters of The Washington Post.

A department official said there are "no plans" to meet with Nzo during his visit. Spokesman Charles E. Redman said the department has no record of a request by Nzo for a meeting.

Redman said the United States maintains "regular contacts" with the ANC but did not elaborate.

The administration has been pressing the South African government to release imprisoned ANC leader Nelson Mandela and begin holding talks with him and other black nationalist leaders on establishing a new political system that would include the nation's black majority.

Nzo was highly critical of U.S. policy toward South Africa, asserting that the administration has not done "anything at all" to assist in the effort to bring about peaceful change.

"At this point in time, the administration is not ready to assist a peaceful transition" to black majority rule, he said.

Nzo also accused the administration of trying to sabotage international efforts to impose economic sanctions on South Africa by shunning, along with Britain and West Germany, a U.N.-sponsored conference on the issue.

Nzo appealed to the administration to abandon its attitude of strong opposition to imposing economic sanctions on South Africa, saying external pressure is needed to force the government to negotiate with the black majority.