President Reagan, who has resolutely resisted demands that he take a tougher stand against the apartheid regime in South Africa, is under increasing pressure from some of his closest allies on Capitol Hill, who fear that his current policies will hurt the Republican Party in the fall elections.

For example, two key Republican senators are pressing Reagan to send a special envoy to South Africa as part of a strategy to defuse pressure to impose new economic sanctions on South Africa. But the White House, unable to agree on who should go or what message should be sent, has put off a decision until later, according to administration officials.

The envoy proposal, made by Sen. Richard G. Lugar (R-Ind.), chairman of the Senate Foreign Relations Committee, and Sen. Nancy Landon Kassebaum (R-Kan.), head of the Senate subcommittee on African affairs, comes when the administration is under the heaviest pressure ever to abandon its policy of "constructive engagement," in force since 1981, in favor of a more activist diplomacy toward Pretoria.

Mindful that 22 Senate Republicans face reelection in November, some GOP strategists want to see the administration modify or scuttle constructive engagement in favor of something more in line with public opinion.

"Republicans want the president to get out front on this issue," said one conservative Republican staff member, who noted that Reagan has never made a major policy speech on South Africa and that Secretary of State George P. Shultz has never visited white or black Africa since taking office in August 1982.

Constructive engagement has emphasized close contacts and quiet pressure on Pretoria to encourage reform by the white leadership. Shultz and Assistant Secretary of State Chester Crocker continue to defend the policy, and fight an increasingly uphill battle against the imposition of stiff economic measures.

Earlier this month the House passed the most stringent economic sanctions bill in its history, which would require all U.S. firms to leave South Africa within 180 days and would impose almost a total trade embargo.

Additional pressure for a change in U.S. policy is coming from a 12-member advisory committee on South Africa set up by Secretary of State George P. Shultz last December. Its cochairman, William T. Coleman Jr., said in an interview that the committee hopes to issue recommendations for new U.S. actions by the end of this summer, rather than waiting until the end of the year as first planned.

A source close to the committee said, "They are taking a serious look at all possible alternatives, including sanctions."

Sen. Paul Laxalt (R-Nev.), who served as Reagan's special envoy to then-President Ferdinand Marcos of the Philippines, said he was ready to carry out a similar mission to South Africa if asked, but quickly added, "I'd want to know it wasn't a purposeless mission."

Laxalt, who has already discussed the idea with Reagan's national security affairs adviser, Vice Adm. John M. Poindexter, said he is not sure what such a mission could accomplish because "it's a confused, complex situation that you can't deal with simplistically."

Reagan's national security advisers are particularly troubled about whether the administration should urge South African President Pieter Botha to open talks with the black nationalist African National Congress because of its links to the South African Communist Party, according to informed sources.

Lugar and Kassebaum particularly want Reagan to take action before hearings on South Africa start in the Senate Foreign Relations Committee July 22. Kassebaum has also urged the president to devote one of his Saturday radio messages exclusively to South Africa.

"Legislative frustration is no substitute for timely and effective leadership in the development of policy initiatives designed not merely to react to the inequities of apartheid but also to promote the process of peaceful change," the two senators said in a letter sent to the White House on Monday.

At least four names have been mentioned as possible presidential envoys: Vice President Bush, former national security affairs adviser Robert C. McFarlane, Shultz and Laxalt.

While House officials said this week it was unlikely that Reagan would follow the same strategy he adopted last year of giving in to congressional pressure at the last moment and imposing a few limited sanctions before a bill requiring far stronger action arrived on this desk. With an executive order last Sept. 9, Reagan banned the sale of South African gold krugerrands in the United States and prohibited new bank loans to the government or any of its apartheid-enforcing agencies.

In a June 24 interview with the Los Angeles Times, Reagan indicated his strong opposition to the House-passed disinvestment bill, saying it would be "truly counterproductive and disastrous" for the United States, "out of sheer pique or anger," to cut off all contact with the South African government.

He also expressed sympathy for Botha, saying the South African had shown willingness to take steps "to rid the country of apartheid" but was being opposed by one faction within his own government. "I have to believe in the sincerity that he wants to find an answer to the problem," Reagan said.

White House officials say a decision on whether to take further steps is unlikely until after the Senate hearings. Until then, they said, it is unlikely Reagan or his national security staff will focus on the options open to the president.

Staff researcher James Schwartz contributed to this report