WASHINGTON (AP) _ Secretary of State George P. Shultz told Republican senators Tuesday that a vote to override President Reagan's veto of South African sanctions will undercut Reagan's ability to negotiate with Soviet leader Mikhail Gorbachev.

The White House, fighting to save the administration's policy of moving slowly on attempts to punish the white-minority government for its policy of apartheid, also announced that Reagan is naming career diplomat Edward J. Perkins, 58, to be the first black American ambassador to Pretoria.

Perkins has been serving as U.S. ambassador to Liberia. He would succeed Ambassador Herman W. Nickel in Pretoria when confirmed by the Senate.

Shultz's appeal for votes to sustain Reagan's veto of tough legislative sanctions against P.W. Botha's government, and the Perkins appointment, seemed to have been coupled with Reagan's offer Monday to issue new but limited sanctions against South Africa by executive order.

It all was part of a campaign by the administration to win the votes needed to sustain the veto in the Senate and stave off an embarrassing foreign policy defeat on Capitol Hill.

Senate Majority Leader Bob Dole, R-Kan., convened the meeting with Shultz in his Capitol Hill office in the aftermath of the overwhelming 313-83 House vote Monday to override the Reagan veto.

''The president should obviously make every effort to sustain the veto,'' Dole told reporters. ''The president is not going to give up on this easily.''

''I asked my colleagues to hold their fire and give the president an opportunity to visit with them,'' Dole said. ''I believe the veto ought to be sustained.''

But in responding to questions, Dole said the battle remains an uphill one. ''He may lose,'' Dole said of Reagan. Dole said Shultz told the group of nine to 10 Republican lawmakers that it ''wouldn't be of any help to the president when he sits down with Mr. Gorbachev to have been clobbered by the Congress on a foreign policy issue.''

Sen. Charles Grassley, R-Iowa, one of the participants in the meeting, said Shultz made ''a very strong pitch that the president's veto ought to be sustained'' and clearly linked the override vote with the Reagan-Gorbachev meeting.

''The secretary said that if the Senate overrides the veto on South Africa it would weaken the president's bargaining position ... in his meeting with Gorbachev,'' Grassley said.

But the senator said he didn't think the argument has much weight because the United States has relations with 172 nations, and ''our policy toward South Africa should not be a driving force'' in talks with the Soviet Union.

''I don't think he found too sympathetic an ear from the nine to 10 of us who were present,'' Grassley said.

When asked if Shultz had changed any votes, Grassley replied, ''No 3/8''

Dole said he is convinced that the president's offer to extend the list of sanctions he imposed by executive order last year represents a significant change in administration policy.

''I think the president now understands that the Congress is not going to let this issue go away,'' Dole said.

But Sen. Richard Lugar, R-Ind., chairman of the Senate Foreign Relations Committee, said the executive order is ''a day late and a dollar short.''

Lugar called on the Senate to promptly override the veto and impose congressional sanctions by law because, ''We are on the threshold of a tragedy that hopefully our timely action will avert.''

Lugar later said he thought the attempt by Shultz to link South Africa sanctions with the Reagan-Gorbachev meeting was ''far fetched.''

''South Africa is not going to be on the agenda with Gorbachev,'' Lugar told reporters. ''That's reaching very far.''

When asked whether Reagan's last-minute efforts to sustain his veto will succeed, Lugar replied, ''No, I don't think they are having any impact.''

Even some of Reagan's closest allies in the Senate said there was virtually no chance the president's veto would be sustained.

The Senate originally voted 84-14 for the sanctions legislation. A two thirds vote is needed to override the veto. The president needs the votes of at least 34 senators to block that two thirds majority and make his veto stick.

Sen. Warren Rudman, R-N.H., told reporters that vote counts show that only 22 or 23 senators are now prepared to support the president's position.

''I don't see where he could get the rest,'' Rudman said.

And Sen. Paul Laxalt, R-Nev., one of Reagan's closest friends in the Senate said bluntly, ''I don't think the president will make it.''

Reagan said he would impose by executive order a ban on new U.S. investments to all South African companies except those owned by blacks, ban the import of South African iron and steel, ban U.S. bank accounts for the South African government or its agencies, review ways to reduce U.S. dependence on strategic minerals from South Africa and provide $25 million in U.S. aid to disadvantaged South Africans.

In contrast, the legislation passed by Congress would ban all new investment and all new bank loans, end landing rights in the United States for South African aircraft, and ban the import not only of South African iron and steel but also coal, textiles, uranium, arms, food and agricultural products. It also would bar the export of petroleum products to South Africa and award the South African sugar import quota to the Philippines.