Johannesburg — The South African government heaved a sigh of relief when Ronald Reagan - favored for his policy of ''constructive engagement'' - and not Walter Mondale was elected president in November.
But the sense of relief is now all but gone, replaced by serious concern in Pretoria over an apparent rising anti-South Africa sentiment in the United States, say businessmen and political analysts familiar with government thinking.
The concern is that the public demonstrations and recent criticism of the Reagan administration's approach to South Africa from Republicans in Congress may have an impact on US policy. The Reagan administration is under fire for not putting more pressure on South Africa to end its segregationist policies.
''There is great concern about (developments in the US),'' says Johan Barratt , director of the South African Institute of International Affairs. ''But I do not think it is having the effect of causing the (South African) government to consider changing its policies.''
Indeed, the only official reaction to the US demonstrations has come from South African Ambassador Brand Fourie, who said last week that his country would never be told what to do by outside pressure groups.
Pretoria prefers the Reagan administration's use of quiet diplomacy in dealing with South Africa and fears any shift to the more voluble criticism characteristic of the last Democratic administration.
The trend in the US underscores how wrong things have gone for the South African government in recent months. Black unrest more serious than the Soweto uprising of 1976 has claimed more than 150 lives, bringing a new focus of world attention on South Africa's unique system of racial segregation called apartheid.
President Pieter Botha has instituted a new-styled government that brought Coloreds (persons of mixed race) and Indians into the previously all-white Parliament. But blacks were excluded. This omission has led virtually all blacks and many Coloreds and Indians to reject Mr. Botha's new deal as bogus reform.
Botha went some way toward building better relations with the West when he visited Europe earlier this year. But his gains appear to be unraveling in the wake of South Africa's internal upheaval of black unrest - and the heavy-handed way the government has dealt with it.
TransAfrica, a black lobbyist group in Washington headed by Randall Robinson, has organized demonstrations in the US against what it calls the ''Reagan administration's indifference to the ravages of apartheid. . . .''
Last week 35 Republican members of Congress warned the Reagan administration and South Africa that they were prepared to work for economic sanctions against South Africa unless there were more urgent moves to end apartheid. Sen. Richard Lugar of Indiana, chairman-elect of the Senate Foreign Relations Committee, and Sen. Nancy Kassebaum of Kansas, chairman of its Africa subcommittee, also sent a letter to President Reagan urging him to speak out more forcefully against apartheid.
Those organizing the public demonstrations at South African embassies and consulates in the US are hoping to spread their campaign to Europe. The Western world's largest trade union body, the International Confederation of Free Trade Unions, has reportedly called for the severing of all economic ties with South Africa.
Despite these pressures, the Reagan administration is apparently staying firm with its policy of ''constructive engagement.'' After a meeting with the President last week, Chester Crocker, US assistant secretary of state for African affairs, said Reagan was ''very supportive'' of the policy.
The most serious concern here is that recent pressures in the US against South Africa will accelerate the already intensifying campaign for the withdrawal of US business investments in this country. That campaign has been building steam for more than a year.
Informed sources in the South African business community say Pretoria has made recent overtures to business leaders, encouraging them to try to sway public opinion in the US against the economic isolation of South Africa.
Many business leaders have told the government only political changes can defuse the cry in the US for a curtailment of economic contact with South Africa. But most are not optimistic about new political initiatives.
Peter Sorour, director general of the South Africa Foundation, a business group opposed to South Africa's isolation, says: ''Even if the government saw an act (of internal change) that could defuse these pressures, and was even prepared to do it, they would hold back for fear of appearing to bow to foreign pressure.''
Last Friday Bishop Desmond Tutu, the South African Nobel Peace Prize-winner, met with President Reagan and urged him to abandon ''constructive engagement.'' He says the policy is being misrepresented.
After meeting with Reagan last week, Dr. Crocker said the administration viewed apartheid as ''repugnant'' but felt the administration's approach of trying to maintain a constructive dialogue with Pretoria stood a better chance of changing South Africa's internal policies.
Right or wrong, the Reagan administration's policy toward South Africa angers many blacks here. ''At no time that I can remember has black opinion of the US (government) been so low,'' says Allan Boesak, a South African theologian.