Civil rights and political activist groups launched a campaign yesterday to persuade Congress and the Reagan administration to impose economic sanctions on South Africa.

A coalition resembling one that fought the civil rights battles of the 1960s argues that if sanctions are suitable for Marxist-ruled Nicaragua they are suitable for white-ruled South Africa.

The campaign against the apartheid policies of South Africa is led by the Washington-based Free South Africa Movement. It hopes to convince Congress that the administration's policy of "constructive engagement" with South Africa -- applying only diplomatic pressure to convince the white-ruled government to change its policies -- is not enough.

"Martin Luther King Jr., I think, is with us today because for many years he talked about the inhumanity of South Africa," said Coretta Scott King. The widow of the slain civil rights leader said she had not seen such solidarity in a movement since her husband fought racism in this country.

Following a day-long strategy meeting of more than 200 groups, Randall Robinson, cochairman of the movement and executive director of TransAfrica, said the campaign was injecting "a new flavor and a new spirit" into an old coalition on behalf of "a new American policy" toward South Africa.

Robinson, King and others, many of whom have been staging protests and vigils in support of South African blacks, told a news conference that they solidly support pending legislation to impose sanctions against South Africa.

The administration's South African policies have come under increasing attack over the last few months, partly because of the publicity engendered by the protests.

The anti-South Africa groups also apparently feel that the administration's position has been further weakened by its decision to impose a trade embargo on the Sandinista government in Nicaragua, which it accuses of exporting revolution throughout Central America.

The administration's difficult position was illustrated earlier this month in testimony before the Senate Foreign Relations Committee by the assistant secretary of state for Africa, Chester A. Crocker, widely regarded as the constructive-engagement policy's chief architect and staunchest defender.

Sen. Paul S. Sarbanes (D-Md.) asked why Crocker continued to defend the policy when so many Americans of all political persuasions had come to the conclusion that it had failed.

"The issues are complicated, but you better start coming to grips with them because you are sitting there . . . in total isolation from what is going on around you," Sarbanes said.

The administration's entire southern African policy -- aimed at getting Cubans troops out of Angola, independence in Namibia and orderly change inside South Africa -- is increasingly under attack from both Republicans and Democrats.

One result is that many Republicans, particularly in the Senate where the terms of 22 GOP members expire next year, are distancing themselves from the administration.

"For most Republicans, the administration's policy provides no political cover," said one Senate staff aide. "The administration isn't even mouthing the right words. Crocker's approach to reform just doesn't sell."

For the first time, there is every indication that both the House and the Senate will pass legislation this session, even over administration opposition, aimed at stepping up U.S. pressure on the Pretoria government.

"Republicans are feeling that the administration's policy has to be altered in some shape, form or manner," said another aide. "There are three or four Republican bills, and these are not liberal Republicans."

Sen. Nancy Landon Kassebaum (R-Kan.), who heads the Senate subcommittee on Africa and is one of the few still opposed to economic sanctions, indicated in an interview that she feels part of the administration's problem is of its own making.

"The least they could do right now is more forcefully speaking out in South Africa, and that we have not done," she said.

In the administration's struggle to head off sanctions against South Africa, President Reagan's decision to impose a trade embargo on Nicaragua has come at an awkward moment. The embargo complicates its argument that such measures imposed on white-ruled South Africa would be "counterproductive."

Democrats in particular have seized upon the apparent contradiction, but the inconsistency troubles many Republicans, who also are pressing for action against South Africa.

"Can anyone seriously doubt that it is far worse to live today as a black man or woman in South Africa than as an opponent of the Sandinistas in Nicaragua," Rep. Stephen J. Solarz (D-N.Y.) said at a House Foreign Affairs committee session just after Reagan announced his Nicaraguan trade embargo.

"If total sanctions are justified against Nicaragua, can we really say that partial sanctions . . . are not justified against South Africa?" Solarz added.

Crocker's answer is that the two cases are different and must be decided partly on the basis of whether U.S. sanctions will make any difference. South Africa's economy is 30 times larger than Nicaragua's and much less vulnerable to the impact of sanctions, he argued.

One gauge of the breath and depth of the South African issue is the shifting attitude among mainstream and conservative Capitol Hill Republicans, many of whom are openly disgruntled with the administration's "constructive engagement" policy.

The Senate's Republican leadership, a group of well-known House Republican conservatives led by Rep. Newt Gingrich of Georgia and another by Mark D. Siljander of Michigan have come out for various kinds of sanctions.

Two conservative Republican senators -- William V. Roth, Jr. of Delaware and Mitch McConnell of Kentucky -- have introduced a bill that calls for banning all U.S. loans to the Pretoria government and all flights by South African Airways to the United States. Licenses of goods and technology for South African nuclear development would be blocked. The bill also would reduce the number of South African consulates allowed to operate here.

The focus of the legislative battle today is in the Senate, where Republicans are in control and the administration normally could be expected to have a better chance to head off legislation it opposes. Even there, however, it is locked in an uphill battle.

Sens. Edward M. Kennedy (D-Mass.) and Lowell P. Weicker Jr. (R-Conn.) have introduced probably the strongest bill to date, but even their proposals do not differ radically from ones put forth by conservative Republicans.

Known as the Anti-Apartheid Act of 1985, the Kennedy-Weicker measure would prohibit all new U.S. loans to South Africa, restrict new investment, prohibit computer sales to the government there and ban the sale of South African gold krugerrands in the United States.

An identical bill has been introduced in the House by Rep. William H. Gray III (D-Pa.) with 145 co-sponsors, seven of them Republicans. It has already been approved by the Foreign Affairs Committee and is expected to reach the floor before the Memorial Day recess.

An alternative approach, more to the administration's liking, has been proposed by the Senate Foreign Relations Committee chairman, Richard G. Lugar of Indiana, and cosponsored by Sen. Charles McC. Mathias Jr. (R-Md.) and Senate Majority Leader Robert J. Dole (R-Kan.).

The thrust of this bill is to increase aid for the economic and social betterment of the black population in South Africa and put off any consideration of economic sanctions for at least two years to give the South African government more time to make reforms.

But it would make the "Sullivan principles" mandatory for U.S. companies operating in South Africa. The principles, named after Rev. Leon Sullivan of Philadelphia, seek to assure equal treatment for blacks and improve their general conditions both in and out of the workplace.

Even this limited step is so far unacceptable to the administration, however.

Crocker told the Senate Foreign Relations Committee May 2 that the Sullivan principles would be difficult to apply and monitor in a foreign country.

The administration's position, as presented by Crocker, is that more change for the better is taking place than ever before in South Africa and that U.S. sanctions would be sending the "wrong signal at the wrong time."