President Pieter W. Botha, responding to widespread calls for urgent changes in South Africa's apartheid system of white-minority rule, tonight said he will not be "stampeded" into reforms. He challenged critics to come forward with "practical, applicable" solutions to the country's problems.

In his first public address since his much criticized hard-line speech in Durban last week, Botha appeared to seek to placate sympathizers in friendly western governments, such as the United States and Britain, without backing away from his tough stance against opponents inside South Africa.

Botha also appeared to call for those he called radicals to take part in "reasonable" negotiations. Although he did not elaborate, and the statement was not in his official text, it was the first time Botha has suggested that such opponents of his government would be allowed at a future bargaining table. "This is the last of these calls that I will make," he said.

The South African president sought to portray his government as a moderate one caught between forces on its left and right. He reiterated his hard line against those "radical communist forces" he said were behind the black unrest that has claimed more than 625 lives in the past year.

We will defeat them for South Africa," he told a cheering crowd of about 1,000 members of the youth wing of his ruling National Party here. "We have the people and the will to do it."

He also sought to bolster the objections to economic sanctions against South Africa by emphasizing the damage such sanctions could have on neighboring black countries.

In a passage that appeared directed at the Reagan administration and "enemies and critics" who have called on him to announce new reforms, Botha said: "Let me tell them, reform does not come overnight. Real stability and development cannot be achieved by the stroke of a pen.

"We shall not be stampeded into a situation of panic by irresponsible elements for opportunistic reasons. We shall not be forced to sell out our proud heritage we built up over decades. Their attempts to make us a pushover will prove to be a march of folly for our enemies."

Botha also pleaded with critics of his Durban speech, saying in a departure from his prepared text, "Don't reject it, read it," implying that there was more to last week's address than most analysts and western governments had recognized.

Then in a further departure from the text, he added: "Think about how South Africa can find a solution to its problem of relations between minorities. Think about how we can ensure the orderly existence of urban black communities. We don't want to stop you from thinking about these things. And if you have proposals, and if they are practical, and if they are applicable, bring them."

Botha's asides, spoken in his native Afrikaans, were clearly designed to give new hope to those -- including Reagan administration officials -- who contend the government has started, however reluctantly, down a path of genuine reform.

Those officials had expressed keen disappointment following his Durban speech, which South African diplomats had billed in advance as promising a major break with previous government policy. The speech itself contained no substantive reforms, only a reiteration of Botha's previous positions and a harsh attack on those he said were pressuring him unfairly for major measures.