Pinning his hopes on American "people power," South African Bishop Desmond Tutu said yesterday he has come to the United States to publicize apartheid atrocities and drum up more support for pressuring the Reagan administration and corporate America to take a tougher stance against white minority-ruled South Africa.

Tutu's campaign to get Americans to open their hearts and pocketbooks on behalf of his antiapartheid struggle got a boost yesterday when leaders of protests outside the South African Embassy announced the start of a boycott against Shell Oil Co. products.

The boycott, organized by the Free South Africa Movement, is targeting Shell Oil in hopes of pressuring its parent company, Royal Dutch Shell, to shut down petroleum and mining operations of Shell South Africa, another Royal Dutch Shell subsidiary.

Tutu is in the midst of a three-week visit to the United States that will take him to 12 cities and major college campuses across the country. In contrast to his visit last year, when he asked for and was granted a meeting with President Reagan, the Nobel Peace Prize winner said he has no interest this time in sitting down with administration officials.

"I want to talk to the people because it has been the people who have forced the administration's hand," Tutu said in an interview with Washington Post editors and reporters.

The 54-year-old Anglican bishop of Johannesburg also credited "people power," including the yearlong series of embassy demonstrations, with getting Congress "to change, quite completely really, in its attitude toward sanctions" against South Africa.

"I think that we are seeing a very interesting development -- people power -- where the vast majority of the people of this country are at variance with their government over this particular issue," Tutu said.

The bishop said American corporations "are going to have to be taking more and more notice of this moral thing which we mustn't dismiss or pooh-pooh."

Tutu has been in close contact with organizers of the embassy protests and met with them Wednesday. His work in South Africa, according to Randall Robinson, a chairman of the Free South Africa Movement, has been an inspiration to apartheid foes for years.

Tutu's United States itinerary includes Philadelphia, Chicago, Detroit, Baltimore, Los Angeles and San Francisco. He also will be traveling to Atlanta to help observe the first celebration of Dr. Martin Luther King Jr.'s birthday as a federal holiday.

Vice President George Bush, who is also participating in the King holiday observance, will be in Atlanta the same time as Tutu, and his office said yesterday that the vice president has asked to meet with the bishop.

"They're both going to be there," a Bush spokesman said. "We do expect them to meet, but it's not as firm as it might be."

Expressing disinterest in meeting with any U.S. government officials, Tutu said he would not "seek out" such encounters during his current visit..

Tutu has long criticized the Reagan administration's policy of "constructive engagement," or quiet diplomacy, with the South African government, calling it "an unmitigated disaster."

Tutu said that because South Africa describes itself as anticommunist, the Reagan administration justifies everything, including the erosion of human rights. "Now I would just hope . . . that the decent people of the United States will say to your government that that's not how you handle things."

In widening their antiapartheid campaign to include Shell, organizers of the boycott said they too are counting on the American people -- to flex their muscles as consumers.

Robinson said the boycott will start Monday, with picketing here and the distribution in several cities of leaflets explaining the action. He said he hopes the boycott of Shell, one of 350 American corporations doing business in South Africa, will persuade the other companies to reexamine their ties there.

"Shell and other corporations which support South Africa and profit from her system of semislave labor must be persuaded by the full force of international revulsion at apartheid to cease doing business there until that evil system is destroyed," Robinson said.

A spokesman for Shell, Bill Lafield, said the Houston-based company does not do business in South Africa and has no influence over Royal Dutch Shell or Shell South Africa.

Lafield called the boycott "clearly misplaced and very unfair." He said the action will especially hurt some 5,500 American Shell dealers or "jobbers" who individually lease and operate almost all of the company's service stations here or who own the property and sell Shell products.

At a news conference announcing the boycott, Robinson was flanked by prominent labor union, women's movement and congressional leaders.

Owen Bieber, president of the United Auto Workers union, said that nearly 1,000 UAW staff members already have cut their Shell credit cards in half and mailed them to the union's headquarters for forwarding to Shell. Leaders of several other unions said they plan to ask their members to do the same.

Robinson said the boycott would continue until American firms in South Africa "come home."

Howard Seney, who operates a service station in Silver Spring and employs 25 people, said he understands the reasons for the boycott and opposes apartheid. "But sympathy is one thing, money out of your pocket is another," he said.