Seventeen persons, including Del. Walter E. Fauntroy (D-D.C.) and U.S. Civil Rights Commissioner Mary F. Berry, were arrested at the door of the South African Embassy here yesterday during a peaceful demonstration to mark the 10th anniversary of the uprising in that country's black township of Soweto.

Fauntroy, Barry and Randall Robinson, head of TransAfrica, handcuffed themselves to metal railings on steps outside the embassy after a rally of an estimated 600 protesters. There were calls for immediate imposition of harsher U.S. economic sanctions against the white minority government of South Africa because of its policy of rigid racial segregation.

In South Africa yesterday, millions of black workers went on strike to commemorate the Soweto uprising.

"This should be a day of shame for South Africa," said Berry. "We are sick and tired of apartheid."

The 1976 riots, in which 176 persons were killed during the first week, have become for South African blacks and their supporters in this country a symbol of recent efforts to overturn that country's policies of racial separation. Yesterday, D.C. City Council Chairman David A. Clarke was among demonstrators who marched along Massachussetts Avenue NW a block from the embassy.

Sen. Gary Hart (D-Colo.), speaking to the group, urged Reagan administration officials to use U.S. economic and military influence to bring about "a transition to black majority rights" in strife-torn South Africa. Hart was not among the 17 protesters who later walked to the embassy door, carrying white wooden crosses and black cardboard coffins representing blacks recently killed in violence in South Africa.

D.C. police used large metal clippers to cut Fauntroy, Berry and Robinson free from the embassy entrance before leading them to waiting patrol wagons.

Also arrested was William Lucy, president of the Coalition of Black Trade Unionists. The 17 were charged with illegally congregating within 500 feet of a foreign embassy and were released pending a court appearance June 23.

Officials in the U.S. attorney's office, who have dropped charges against all of the more than 3,000 protesters arrested at the embassy since organized demonstrations began there in November 1984, yesterday declined to comment on whether any of the 17 persons arrested yesterday would be prosecuted on the misdemeanor charge.

On Capitol Hill yesterday, officials of several U.S. religious denominations and church groups who are preparing to lobby for proposals that would legislate stiffer sanctions against South Africa were briefed by congressional leaders. South African exiles and students were scheduled to meet last night at Howard University.

The Pretoria government's declaration last week of a state of emergency outlawing all gatherings appeared to reinvigorate protesters here, who had ceased their daily demonstrations near the embassy late last year and seemed to be making little headway in efforts to organize boycotts of U.S. companies doing business with South Africa.

Robinson, a chief organizer of the embassy protests as well as antiapartheid efforts nationwide, aimed some of his harshest criticism at President Reagan and other U.S. officials who have condemned the new repression in South Africa but have declined to impose stiffer sanctions.

"The president cannot find the commitment, cannot find it in his heart to even criticize the most vicious nation on earth," Robinson said. "We as a nation have become the legs on which apartheid walks."