South Africa's Bishop Desmond Tutu thanked American apartheid protesters yesterday for "putting your bodies where your mouths are" and said he is grateful to those demonstrators at the South African embassy who have embraced a cause for which he recently won the Nobel Peace Prize.

"Whatever you do to protest this evil system does not go without notice among those for whom it has been done," said Tutu, the guest speaker at a special Washington Cathedral service honoring his award. "So thank you. God is good."

Tutu said he had not asked American black leaders to organize the demonstrations and arrests now taking place at the South African embassy. But he said he is glad they did.

"I just said to people, 'For goodness sakes, put your act together,' " Tutu said.

The Washington Cathedral service was attended by D.C. Del. Walter E. Fauntroy and Randall Robinson, executive director of TransAfrica, a lobbying group on African and Caribbean concerns, both principal organizers of the embassy protests, and by Jesse Jackson, long a critic of the South African government's policies of racial segregation.

Jackson blasted the Reagan administration earlier yesterday for its "cozy kinship" with the government of South Africa and praised organizers of the embassy demonstrations. He also said he is calling off a planned visit to the embassy today so as not to detract from the continuing protest there.

But Jackson said he did not plan at this time to join other demonstrators who have been going to jail to protest South Africa's policies of racial segregation and that "the judgment has not yet been made" on whether he will take part in picketing at the embassy.

A Baptist minister who campaigned for the Democratic presidential nomination this year, Jackson said he had canceled an appointment with South African Ambassador Bernardus Fourie to discuss his long-stalled request for a visa to visit the country.

"We're still appealing to go," Jackson said at a news conference after services at the Shiloh Baptist Church. "But given the heightened demonstrations this week at the embassy, to go across the picket line would divert attention from this substantive demonstration."

Hours before Jackson's news conference, sources close to organizers of the embassy protest expressed concern that an embassy visit by the charismatic black leader might upstage or complicate plans to broaden the anti-apartheid campaign. There also was concern, sources said, that Jackson was preparing a maverick move to visit South Africa and try to secure the release of 13 jailed black trade unionists, whose release is a top priority for embassy protesters.

"He could ride up to the movement, no team play, go to the head of the line . . . and could ride off into the sunset," said one organizer, expressing concern that Jackson would arrange his set of South African concessions that could slow the momentum of recent protests.

Fauntroy and Robinson were conspicous by their absence at Jackson's news conference, and Fauntroy said later he was concerned that the South African government might try "to defuse our movement" by extending an invitation to Jackson to visit the country. But he and Robinson denied any rift over Jackson's own South African agenda, saying that scheduling conflicts had prevented their appearance with him.

"Jesse has demonstrated in the clearest of fashions that we are not going to be divided," said Robinson. "We are of one mind."

Since Nov. 21, almost daily protests culminating in a few arrests each time have been staged at the South African embassy. Today's demonstrations, organized as part of the "Free South Africa Movement," are scheduled to spread to South Africa's consulates in this country.

Among the 16 people arrested during the embassy demonstrations, in addition to Fauntroy and Robinson, have been Reps. Charles Hayes (D-Ill.), John Conyers Jr. (D-Mich.), Ron Dellums (D-Calif.), and Don Edwards (D-Calif.), Gerald W. McEntee, president of the American Federation of State, County and Municipal Employees, and Yolanda King, daughter of slain civil rights leader Martin Luther King Jr.

Charges against all but two of the demonstrators were dropped Friday and Saturday by U.S. Attorney Joseph E. diGenova, who said the cases were not worth prosecuting.

The jailing of prominent clergy, political and labor leaders, Jackson said yesterday, "is a magnificent nonviolent witness against the U.S. partnership with the racist apartheid regime." And the subsequent dismissal of charges against them, he charged, is an obvious attempt to avoid jury trials, "which could prove to be quite embarrassing" to South African and U.S. officials.

Jackson credited TransAfrica with focusing unprecedented attention on the South Africa problem but said earlier efforts by the Student Nonviolent Coordinating Committee and black leader Malcolm X had laid the groundwork.

"We're seeing the blossoming of flowers that have been budding for years," he said.

The Reagan administration, following a policy it calls "constructive engagement," says it abhors South Africa's apartheid policies but wants to improve relations with the government and seek reforms over a longer period of time.

But Jackson complained that the United States and U.S. corporations derive billions of dollars in trade and other business associations with South Africa and said he plans to seek a meeting with President Reagan to discuss "a new Africa policy." He said also that he has started meeting with Catholic officials in hopes of convincing Pope John Paul II to reaffirm his condemnation of apartheid and to visit South Africa.

Pointing out his interest in visiting the country to meet with its leaders, however, Jackson said he could not get arrested and be jailed during an apartheid demonstration at the embassy while he is trying to get that embassy to grant him a travel visa.

Tutu, who gave the sermon at the service, said he was given the Nobel Peace Prize not for himself but as symbolic recognition"for all who struggle for justice and peace and reconciliation."