Three months after the South African government introduced a new national constitution modifying its segregationist system called apartheid, three special election results announced today showed that it is losing many of its traditional white Afrikaner supporters to the far right Conservative Party.

Although the ruling National Party won all the whites-only elections, which were to fill vacancies in the national Parliament, its majority was reduced each time in districts where most of the voters are Afrikaners.

President Pieter W. Botha claimed the victories gave his government a mandate to continue with its program of cautious reforms, but many observers predicted that the loss of Afrikaner support would alarm it into moving even more tentatively.

The most telling result was in a constituency called Primrose, in the industrial city of Germiston, near Johannesburg, where the government's majority was cut from a safe 4,399 at the last general election in 1981 to an uncomfortably slender 748.

Polling analysts say this means that the Conservatives could increase their representation from 12 to 40 in the 177-seat Parliament if a general election were held now.

This poses no immediate threat to the Botha government, which has a parliamentary majority of more than 100 and under the new constitution need not call a general election until 1989.

But it exercises a strong psychological effect on the National Party, which has a deep-rooted fear of losing the struggle for the soul of the Afrikaner people to the Conservatives.

Forty seats also would be enough for the Conservative Party to replace the liberal Progressive Federal Party as the official opposition in Parliament.

The government suffered another setback in two other special election results announced today, when many members of the mixed-race community known as Coloreds again failed to vote for parliamentary seats allocated to them under the new constitution.

While white conservatives have opposed Botha's constitution for being too liberal, nonwhites have opposed it as a sham because it gives voting rights only to the Colored and Asian minorities and continues to exclude the black African majority.

Black leaders called for a boycott of elections held for these minority groups under the new constitution last August, and only 30 percent of registered mixed-race and 20 percent of registered Asians voted.

In the special mixed-race election results announced today, the voter turnout fell well below the August percentage in both districts.

The Conservative Party was formed just over two years ago when Andries Treurnicht, then leader of the ruling party's stronghold province of Transvaal, led a breakaway movement to protest Botha's constitutional plans.