White South Africans reacted with surprise and delight today to President Reagan's speech yesterday rejecting economic sanctions as a way to force an end to the government's policy of apartheid, but black leaders were furious at what they regarded as a major letdown by the West.

The government's satisfaction over the Reagan speech was also heightened by its timing, coming just hours before the arrival of British Foreign Secretary Geoffrey Howe on a mission from the European Community that is also aimed at trying to avert economic sanctions against Pretoria.

Most black leaders, including Bishop Desmond M. Tutu, have said they would refuse to meet with Howe and that they view his visit as a way for Britain to mitigate the pressure for sanctions from some of its partners in the European Community.

Analysts here said Reagan's strong stand against sanctions would help Howe's mission and would make it easier for British Prime Minister Margaret Thatcher to withstand pressure for sanctions from within her own party and opposition parties, as well as from the community.

The government's sense of relief was palpable, as officials, who have been increasingly anxious recently under the strain of the continuing racial conflict and foreign condemnation, smiled and joked as they waited for Howe's plane to land at the Johannesburg airport.

Foreign Minister, Roelof F. (Pik) Botha was beaming. Asked why he looked so pleased, he quipped, "I can even smile when things are tense."

Last night the foreign minister issued a statement welcoming Reagan's speech and suggested that it opened the way for South Africa to have talks "at the highest level" with the United States and other countries "regarding the realities of Southern Africa."

This was followed today by a chorus of statements from white business leaders lauding the Reagan speech as "a note of realism" and saying U.S. opposition to sanctions would help South Africa develop a stable society.

"I think the most important thing about President Reagan's speech is that it has lifted a siege mentality that had taken hold here," said Carl Noffke, a former Washington-based diplomat who is now director of the Institute of American Studies at Johannesburg's Rand Afrikaans University.

Noffke said he believes the administration of President Pieter W. Botha had resigned itself to the inevitability of sanctions and was adopting a "to hell with the world" attitude. The government expected Reagan to announce a tough new policy to replace "constructive engagement," and the sense of relief when he did not has dispelled the siege mentality, Noffke said.

"Now there is a feeling that we have at least two friends in the world Reagan and Thatcher who are willing to listen before they introduce any sanctions," the former diplomat added.

Noffke also said the administration now feels its action in declaring a state of emergency has been justified. It had taken this tough action expecting that it would produce a strong international reaction and probably sanctions, but the attitude adopted by Reagan and Thatcher has shown that the worst was not going to happen.

"The government is winning the battle so I don't think the emergency is going to be ended soon. I think it will continue for a while," Noffke said.

He added that Reagan had "done a great public relations job" for South Africa by stressing the country's importance to the West before an audience of millions. "He did a better job for us than we have ever been able to do for ourselves," the former diplomat said.

Tutu, however, was not mollified by Reagan's sharp criticism of apartheid during his speech. "I think it's quite disgusting to express ritual abhorrence of apartheid and then to hear all this nonsense that we will be the first ones to suffer from sanctions."

Other black leaders, some of whom are in hiding to avoid detention under the emergency regulations, expressed fears that the government would now feel it was safe from any serious prospect of sanctions and would crack down more severely than ever on black activists.

The United Democratic Front, the main alliance of black activist movements which has borne the brunt of the emergency crackdown, issued a statement accusing Reagan of siding with repression.

"After his support, even with weapons of death, for Unita in Angola and the contras in Nicaragua, how can President Reagan attempt to convince us that he stands for peaceful change in South Africa?" the front said.

One black leader who praised Reagan's speech was Chief Gatsha Buthelezi, the influential Zulu chieftain who strongly opposes sanctions. In a brief statement, Buthelezi said the president had shown that he was committed to the abolition of apartheid "not just through rhetoric but through realistic strategies."

The 50-member Organization of African Unity reacted sharply to the address, which it said represented a "covert support for racism" and appealed to the U.S. Congress to impose sanctions on its own.

Speaking to the foreign ministers of the OAU, Nigerian Foreign Minister Bolaji Akinyemi said Reagan's message was "a calculated attempt to arrest the momentum of both international and American opposition to apartheid by resurrection of the discredited policy of construction engagement."

After meeting with President Botha for two hours, Howe characterized the talks as "candid, courteous and substantive." He said he was not here as an outsider trying to prescribe solutions to a sovereign, independent country but "as an intensely concerned friend."

Meanwhile, the government's Bureau for Information, the only authorized source of news about racial unrest under the state of emergency, announced today that six more blacks died in violent incidents yesterday.