Blacks and whites cast the final ballots today in the election that will give Rhodesia its first black prime minister, pushing the total voter turnout in the week-long balloting past 60 percent.

Some observers had predicted a turnout of as few as 20 percent of the eligible voters, but by the end of the fourth day of voting Friday, 1.74 million people, 59.9 percent of the total electorate, already had voted, and election officials predicted the final total could be as high as 65 percent.

The large turnout appeared to be a significant vote of confidence in black majority rule and a victory for Prime Minister Ian Smith, who organized the elections against the wishes of the United States and Britain.

Washington and London have refused to recognize the elections because they excluded black nationalist guerrillas and would not end the six-year guerrilla war.

Offical counting of ballots was slated to start Monday. Virtually all politicians predicted a major victory for the United African National Council and said its leader, Methodist Bishop Abel Muzorewa, will be the next prime minister.

At sundown after the polls closed, white officials lowered the green, white, black and gold flag in front of Government House, symbolically marking the end of five generations of white rule in Rhodesia.

Rhodesian voters were asked to name the 72 black members of a 100-man parliament. The other 28 seats were reserved for the white communnity, 4 percent of the electorate, for a transitional period that could last 10 years.

Some election officials said the immense public response to the election was more a referendum for peace than the voting into power of a new government.

The balloting went smoothly, despite guerrilla attempts to disrupt the voting with widely scattered attacks against polling stations and the burning down of some villages whose population went to the polls.