JOHANNESBURG, South Africa (AP) _ President P.W. Botha said Monday his white-minority government could put a million Americans out of work by withholding chromium exports to the United States.

He was responding to the limited economic sanctions imposed by the United States in September and by the Commonwealth of Britain and 48 of its former colonies Sunday night.

''By digging a hole for South Africa, they could end up harming themselves,'' Botha said at a political rally in the farming community of Bethlehem 130 miles south of Johannesburg.

''The world should cooperate with South Africa in the interests of the whole of southern Africa,'' he said.

Reference books indicate that in 1983, South Africa had 91 percent of the world's chromium reserves. Neighboring black-ruled Zimbabwe, the Phillipines, the Soviet Union and its neighbor, Finland, each had 2 percent.

Botha, speaking in Afrikaans that was translated by the independent South African Press Association, said that withholding chromium exports also could bring Western Europe's auto industry to a standstill.

South Africa is the major supplier of chromium and some other strategic metals needed in the West. Experts disagree on that dependence, however. Some say it is exaggerated by South Agrica, while others claim South Africa is virtually the exclusive supplier of some sophisticated metal alloys used to manufacture modern weapons.

In Detroit, General Motors Corp. spokesman Don Postma was asked about Botha's claim that a South African export embargo could affect a million American workers and he said, ''There's no way of knowing at this time. There isn't any way to evaluate it. We'll just have to see what he (Botha) means by this.'' He also said he didn't know if GM gets its chrome from South Africa.

Other U.S. auto industry spokesman could not be contacted for comment Monday night.

The Commonwealth, holding a summit meeting in the Bahamas, approved a series of mild sanctions against South Africa involving arms and oil sales, nuclear cooperation, governnment loans and trade mission.

But it agreed to review the sanctions in six months and consider firmer action if Botha's government does not accelerate its dismantling of the laws on apartheid - racial separation.

Botha told the Bethlehem rally, ''We will not accept any notice to complete discussions (on changing apartheid) within six months. Only South Africans will decide that.''

He again rejected any one man-one vote system for South Africa, where blacks have no vote and, according to the government, are citizens of black homelands and not South Africa.

And he rejected the idea that a fourth chamber be established in Parliament for blacks, who outnumber whites 24 million to 5 million.

Last year, the government created two additional legislative chambers, one for people of Asian descent and one for those of mixed race. But the white legislature can still block any action by those two chambers.

Botha was campaigning in Bethlehem because a special election there on Oct. 30 pits his National Party against a candidate of the Conservative Party. The Conservative Party was formed in 1982 by whites who claimed Botha's moves to relax apartheid meant he was abandoning white interests.

Botha has told South Africa's Western trading partners that if his government moved too quickly to soften the apartheid laws, some of his National Party members would defect to the Conservatives.

His speeches in the Bethlehem campaign portray the National Party, in power since 1948, as firm and quick to tell overseas critics to mind their own business.