The Free South Africa Movement brought its antiapartheid campaign to the Deep South today, where demonstrators got a message of support from Gov. George Wallace and knelt in prayer at the door of an American businessman who helps promote South African trade in this bustling Gulf Coast port city.

After trying unsuccessfully to meet with the businessman, who serves as one of South Africa's eight "honorary" consuls in this country, the protesters left a downtown bank building but vowed to return, probably Friday.

There were no arrests, though there was considerable gawking and some hostile scowls from townspeople who haven't seen a civil rights protest of this sort in 20 years.

"We have made our statement to this community, and we'll be back," Dr. Joseph E. Lowery, president of the Southern Christian Leadership Conference, said late this afternoon as the demonstration broke up. He called Mobile the "bloody gateway to the South" and said its bay "is stained with the blood of our brothers and sisters in South Africa" who mine so much of the coal unloaded on the city's docks.

At a news conference this morning announcing the demonstration, Lowery, D.C. Del. Walter E. Fauntroy and other SCLC leaders said they were beginning what they call the "Southern wave" of protests that have been a daily occurrence at the South African Embassy in Washington since Nov. 21.

A demonstration is planned for Friday in Houston and Lowery will lead another protest in New Orleans next week. Protest organizers said black leaders already have begun to meet with bankers and other business officials in Atlanta to urge them to drop their financial ties with South Africa.

"We must correct apartheid not only because it is morally reprehensible but because it threatens American jobs," Fauntroy said. "While jobs are being lost in the Birmingham steel mills, they are being opened up in South Africa by American firms attracted by the slave market there."

Fauntroy had to leave town before the demonstration because of a previous commitment. But his brief stay in Alabama was greeted with all the hospitality Wallace never showed when black civil rights leaders of the 1960s first came into his state talking integration.

For the SCLC, which is holding its state convention here, there was a welcoming message, praising its continuation "in the spirit of Martin Luther King," its founder.

And for Fauntroy, there were two proclamations from the governor: one making him an honorary citizen of Alabama, the other heralding him as an honorary lieutenant colonel in the state militia.

But most importantly, as far as its organizers were concerned, there was a message of "moral support" that an aide to the governor delivered at the news conference.

Though Mobile escaped the notoriety that marked Selma, Montgomery, Birmingham and other Southern cities during the civil rights movement, it has had its share of Ku Klux Klan terrorism, some as recently as two years ago. Blacks here today said they regard the city as no less racist than elsewhere, just more subtle about it -- sometimes.

"We still have had local stores who say they can't find a qualified black to work the cash register," said Ernest (Bud) Morrison, president of the SCLC's Mobile County chapter.

The sight of demonstrators picketing in the heart of the town, across from Bienville Square, was met with astonishment by most of those who happened upon the small band of 50 protesters as they paraded in a circle on the sidewalk in front of the First National Bank building and sang booming chorus after chorus of well-known spirituals and civil rights anthems.

"I don't think there's a whole lot they can do, it's been going on over there a long time," said Keith Hedrick, a 28-year-old bank auditor. "I think it has to be a gradual change, like it was here."

Hedrick watched the demonstration from another bank building across the street and his group of white friends seemed to agree with him.

"They need to worry about black people and white people with problems in this country," said Philip Davis, 23, whose words were interrupted -- by him -- when the protesters started singing again.

"Here they go -- 'We Shall Overcome,' " he said, somewhat mockingly.

When a small group of the protesters, including comedian/activist Dick Gregory, took the elevator to the building's 23rd floor to see the honorary consul, John H. vanAken, they found his office locked and his door sporting a South African coat of arms.

After knocking several times and getting no answer, the group knelt and prayed in the narrow hallway.

"If he has a conscience, he must be at least a little uneasy at what he's doing," said Lowery during the prayer. The group stayed about 20 minutes praying and singing songs softly outside vanAken's office. Employes working elsewhere on the floor said they had not seen vanAken all day.

A Mobile police officer on hand to monitor the protest said police would not arrest the demonstrators unless asked to do so by the building managers. When no such request came, the group left.

"He may flee from us but he can't flee from the wrath of God," said Lowery.

Throughout the day, there was excited talk about the success of the antiapartheid campaign so far and repeated criticism of the Reagan administration for its policy of constructive engagement, seeking reforms gradually.

"It's a policy, really, of all carrot and no stick," Fauntroy complained. The United States' problem is not colored people on welfare but rich people who have been investing in a racist country."

South Africa's embassy in Washington and its four consulates in the United States are staffed by South Africans whereas "honorary" consuls are Americans who have been appointed to these posts because of previous ties to the country and a willingness to represent its interests here. Consuls receive no salary but are paid office and other expenses.

VanAken is not the first of South Africa's consuls to be targeted by antiapartheid demonstrators. His counterpart in Boston announced plans to resign a similar post after protesters visited his law office earlier this week.

And in Seattle, Joseph M. Swing, the honorary consul there, says he has been seeing such protests for weeks. "They've been coming every Saturday since September, but the numbers have increased significantly since the demonstrations at the embassy in Washington," said Swing.

Swing, who works out of his home, said recently that he enjoys the work he does for South Africa and leaves questions about apartheid "to Washington."