South Africa's white minority government cannot continue to run the country "with guns" and has delayed too long in beginning negotiations with leaders of the black majority, Chester A. Crocker, assistant secretary of state for African affairs, said yesterday.

In a television appearance, Crocker defended President Reagan's policy of "constructive engagement" with South Africa -- economic cooperation coupled with friendly persuasion to bring about an end to apartheid.

"We are against this kind of killing by the police of unarmed demonstrators," he said of the killing of 19 blacks by South African police on Thursday.

"There is no question whatsoever that that kind of action, belief or use of force by police, as the first recourse in the event of that kind of situation developing, is unacceptable."

Reagan drew fire from black groups for his answer to a question at Thursday night's news conference in which he appeared to lay blame for the violence on both sides. As a result, outraged black leaders in South Africa reportedly refused to meet with Crocker, who was visiting there.

Crocker, appearing on ABC's "This Week With David Brinkley," said the administration is not relying solely on "governmental intentions" but "on our analysis of what's going on in South Africa . . . . If there is not constructive change, there is going to be chaos, there is going to be anarchy, there is going to be a blowup, and that's the key pressure for change.

"The white minority cannot run it with guns," he added. "They cannot run it on the basis of a labor force that's overwhelmingly black," unless there is negotiation and dialogue. "It's been delayed much too long."

Appearing with Crocker were South Africa's ambassador to the United States, Bernardus Fourie; Sen. Lowell P. Weicker Jr. (R-Conn.), and Randall Robinson, executive director of the antiapartheid organization TransAfrica.

Crocker took issue with Weicker and Robinson, who said that U.S. economic sanctions against South Africa would be effective in pressuring the white minority toward an accommodation with blacks.

"Ultimately our leverage . . . is political and psychological, not coercive in the direct physical sense."

Of Thursday's shootings, Fourie said that, contrary to some news reports that the demonstrators were unarmed, they were pelting the heavily outnumbered police with "petrol bombs" and stones and "were marching towards an area where ostensibly they were going to cause destruction," when police opened fire.

Black leaders said the shootings were unprovoked.

The shootings occurred in Uitenhage, when about two dozen police fired automatic rifles, pistols and shotguns on a crowd of about 3,000 blacks gathering to mourn a slain black activist.

Fourie said his government has made it clear that it is willing to negotiate with black leaders to find some way for the black majority "to play a part in the decision-making at the highest levels."

But, he said, "We've got to move cautiously, we've got to move deliberately and we've got to be sure we don't leave behind a situation that is worse."