The Rev. Jesse Jackson, eager to take a group of church leaders to strife-torn South Africa, yesterday urged the government of that white-ruled nation to allow him to enter the country shortly after next month's presidential election.

Jackson, speaking to a crowd of about 150 people gathered near the South African embassy for a demonstration and prayer vigil, warned that he would step up demonstrations here if the South African government denies his request for a visitor's visa. South Africa has been rocked by recent unrest linked to constitutional changes that include Indian and mixed-race citizens into its parliament but excludes the country's black majority.

"The apartheid regime over the past several weeks has been conducting mass arrests and ordering detentions of religious and political leaders protesting the racist policies of the regime," Jackson said.

Jackson also criticized the recent decision made by Herman Nickel, the U.S. ambassador to South Africa, to refuse the requests of six black South African leaders for refuge in the United States. Jackson said human rights in South Africa "must be measured by the same yardstick" as human rights in Poland.

A "Tarzan policy" toward Africa must end, Jackson said, adding that he will urge President Reagan and Walter F. Mondale to make South Africa a "centerpiece" of their upcoming foreign policy presidential debate.

Jackson also threatened protests if a black reporter is not among the panel of journalists who will question Reagan and Mondale at their Oct. 21 debate.

Earlier in the day, at a cordial 10-minute meeting with South African Ambassador Brand Fourie, Jackson said he was told that permission for him to travel through South Africa would require special attention from high-ranking government officials. Jackson said he made his request several weeks ago.

But Fourie, in a telephone interview, said Jackson was told that it would be "inopportune" for him to enter the country this year, and refused to elaborate. Fourie said that Jackson "never mentioned" plans to increase protests if a visa was not granted.

Jackson said he and a small group of church leaders want to meet with South African church and labor leaders, educators and government officials. Specifically, Jackson said he wants to talk with South African Prime Minister P.W. Botha, imprisoned African National Congress leader Nelson Mandela and to his wife, Winnie Mandela, who has been placed in political and social exile.

"If we cannot get into South Africa we must stand here and protest our inability to communicate," he said. "We simply must put our bodies on the lines as living sacrifices to show just how serious we are . . . .