Seven persons, including a Maryland congressman here and four demonstrators in New York, were arrested yesterday as an ongoing protest against apartheid in South Africa spread to a second city and picked up steam with the announcement of similar demonstrations today in Boston and Los Angeles.

"I don't want my country stained with the filth that dominates the government of South Africa," said Rep. Parren Mitchell (D-Md.), who became the latest congressman arrested outside the embassy as the protest entered its third week yesterday. "I think my country needs to hang its head in shame."

Arrested with Mitchell were comedian/activist Dick Gregory and Joslyn N. Williams, president of the Greater Washington Central Labor Council.

Arrested in New York were black leaders David M. Dinkins, the city clerk of New York; the Rev. Herbert Daughtry, president of the National Black United Front; former Judge William Booth, president of the Coalition of 100 Black Men, and Harriet R. Michel, head of the New York Support Committee for TransAfrica. They were taken into custody as they attempted to present a list of demands at the South African consulate.

Picketing and arrests have become a late afternoon ritual at the South African embassy here, and organizers of the antiapartheid protest said yesterday that 12 other cities will be holding such daily demonstrations within the next week and a half.

The growing protest also appeared to have struck a nerve at the White House, where a top State Department official held a briefing yesterday to defend the Reagan administration's policies of "constructive engagement" with South Africa.

Leaders of the Free South Africa Movement escalated their foreign policy battle with the White House yesterday, holding a morning news conference at the embassy to denounce a decision by federal authorities not to prosecute most of the 23 demonstrators arrested so far in the protests against South Africa's policy of racial segregation.

Randall Robinson, executive director of TransAfrica, a lobbying group that is coordinating the antiapartheid protest, argued that dismissing the charges avoids jury trials that might put the South African and U.S. governments on the spot.

"South Africa . . . does not want to discuss in court the whereabouts of those 21 labor leaders, perhaps tortured, perhaps dead, or why the right to vote is denied 70 percent of its people," Robinson said. "And the Justice Department does not want to air the extent to which our own government underpins that vicious system."

Robinson, D.C. Del. Walter E. Fauntroy and U.S. Civil Rights Commission member Mary Frances Berry, the three black leaders whose arrests at an embassy sit-in Thanksgiving eve set the protest in motion, said at the news conference that the demonstrations will continue indefinitely. And -- in response to a warning from Justice Department attorneys that repeat offenders at the embassy would be prosecuted -- they said they may well go to jail a second time if that is what it takes to get a jury trial.

U.S. Attorney Joseph E. diGenova announced last week that he was dismissing the embassy arrest cases, in part because the South African Embassy refused to press charges and because he felt the cases lacked "prosecutive merit" compared to more serious crimes that require the court's attention.

Since then, his office has been dropping charges against the demonstrators almost as fast as D.C. police are arresting the protesters.

"I was looking forward to going to trial," said Berry, who charged that the Reagan administration's policy on South Africa "amounts to winking its eyes" at apartheid.

Since Nov. 21, when Fauntroy, Robinson and Berry were arrested and jailed for staging a sit-in at the embassy, the antiapartheid protest has grown in size and attracted media attention to the point where organizers say they are having trouble "scheduling in" all the people who have volunteered to go to jail on behalf of oppressed South Africans.

Drawing on the lessons and tactics of the 1960s, when America's own civil rights struggle was both painful and public, black leaders here say they are now determined to help spread change abroad -- and to safeguard hard-won gains at home.

"We have struck a deep commitment in the black community to return to direct action," said Robinson. "And it will have implications beyond the issue of South Africa."

TransAfrica, established by black Americans seven years ago to lobby on foreign policy and other issues affecting Africa and the Caribbean, is credited with getting the new apartheid protests off the ground. The Washington-based group, which has about 10,000 members, is the only black American lobby on policies affecting blacks in the Third World.

But as part of the Free South Africa Movement, TransAfrica has been aided in its efforts by a network of civil rights, religious, labor and political organizations, some of which didn't exist 20 years ago.

The Congressional Black Caucus, for instance, is largely the result of civil rights successes of the past. And it is not surprising, said Fauntroy, that black members of Congress have been so willing to help blacks in South Africa win the voting and social rights blacks here were once denied.

Organizers say they began the embassy protests and arrests out of concern that Ronald Reagan's reelection -- and what they regard as his tacit cooperation with South Africa's apartheid policies -- has led to increased repression of South African trade unionists and other blacks. Scores of protesters against the white minority government have already been jailed and tortured, organizers claim, while the U.S. government appears to look the other way.

In addition, blacks in Congress were particularly angry at the Senate's failure to approve a measure that would have prevented U.S. companies from investing in South Africa. Such investments, they argue, buttress South Africa's apartheid economy and result in the loss of jobs for U.S. blacks and other American workers.

And finally, protest leaders acknowledge, the awarding of the Nobel Peace Prize to Bishop Desmond Tutu of South Africa has re- inspired antiapartheid groups here and abroad.

In setting up demonstrations here and elsewhere, TransAfrica has relied on established organizations long involved in antiapartheid or other civil rights activities.

In Washington, the Southern Africa Support Project has handled the daily task of lining up picketers, drawing sympathizers from area universities and from several local labor unions. Fauntroy has coordinated the participation of congressional members, and he and Robinson have the most say about who will be arrested and when.

TransAfrica representatives in other cities, helped by the Coalition of Black Trade Unionists and local church leaders or other black professionals, have shouldered most of the responsibility for organizing demonstrations outside of Washington.

Though the protests here seem well-orchestrated, right down to the finer points of a police escort to the embassy's front door, the organizers say all is not as finely tuned as it appears.

"We know who's going to be on the picket line," said one TransAfrica organizer. "But we don't always know who's going to be arrested until just before it happens."

The spirit, this organizer said recently, "has moved people in different ways. "I've been surprised . . . some have said they couldn't possibly be arrested -- and then have changed their minds" at the embassy. "Others have been all set, and then they get there and say, 'Maybe not today.' "

The important thing, organizers say, is to balance the schedules and affiliations of those willing to be arrested, and to space out the big name officials or celebrities to keep the media's attention.

Mitchell, the sixth member of Congress to be arrested at the embassy, was released late yesterday while Gregory and Williams opted to spend the night in detention at the city's 2nd District police station.

But for every VIP in the ranks of the arrested, there have been less famous but no less committed protesters on the picket line. The demonstrators have been young and old, black and white, handicapped, students, businessmen, unemployed persons, veteran protesters and novices.

"I've never done anything like this before," said DiMaio Amos, 26, a high school teacher from Wheaton. "It's scary. I consider myself a basically conservative person, but this is different . . . . It's not just a race question. It's a human issue."

Mindy Blandon, a nurse at the Washington Hospital Center and secretary of the D.C. Nursing Association, said she and a handful of other nurses came to the embassy protest yesterday "to oppose the jailing of unionists in South Africa, to oppose the system of apartheid there and the support the Reagan administration gives it."

In pressing their case against the Reagan White House at their news conference yesterday, protest leaders attacked U.S. abstention from a United Nations vote against apartheid. They also charged that the administration has trained the South African Coast Guard and shipped hundreds of "shock batons" to South Africa to control the black population.