As President Reagan's foreign policy agenda brims over with the problems of South Africa and the Nov. 19-20 summit meeting with Soviet leader Mikhail Gorbachev, the administration also is being forced into an imminent, all-out effort to salvage its Middle East initiatives from failure.

At stake are the administration's intertwined plans for new arms sales to Saudi Arabia and Jordan despite opposition from a skeptical Congress, and hopes of reviving the moribund Mideast peace process by fostering direct negotiations between Israel and a joint Jordanian-Palestinian delegation.

Progress toward peace talks depends on the United States selling arms as a good-faith gesture toward Jordan's King Hussein and his Saudi allies, according to administration strategists. But Congress now appears to believe that there should be no approval of a Jordanian arms package unless Hussein first moves closer to the bargaining table.

The congressional attitude has been made unmistakably clear to the administration by such key Republicans as Senate Foreign Relations Committee Chairman Richard G. Lugar (R-Ind.). Last week, he bluntly told Secretary of State George P. Shultz that if Reagan goes ahead with the arms-sale proposals under present circumstances, the administration almost certainly will end up expending precious political capital in a long, futile fight.

Despite Lugar's warning that Reagan would be "shooting himself in the foot," the administration intends to plow ahead in a way that seems certain to provoke a major clash with Congress before the end of the month.

That intention was signaled Tuesday by Richard W. Murphy, assistant secretary of state for Mideast affairs. He reportedly hinted to a closed House panel that official notification of the first proposed sale, a package of various missiles for Saudi Arabia, will be sent to Congress shortly after the Jewish high holy days end on Sept. 25.

Other State Department officials said yesterday that, barring a last-minute change of plans, the notification is likely to be made on Sept. 27. The request for Jordan, which is expected to exceed $1 billion, would follow shortly afterward; an additional request to provide Saudi Arabia with advanced F15 jet fighters is tentatively planned for later in the fall.

One official said Shultz and other senior policy-makers believe the administration no longer has the option of further delay.

The administration believes that with Congress expected to adjourn in November, this will be the last chance to keep its long-delayed promises to act on the arms requests this year. The administration also is aware that Israeli Prime Minister Shimon Peres, who wants talks with Jordan, is due to be replaced next year by his coalition partner, Foreign Minister Yitzhak Shamir, who is more hostile to the idea of negotiations.

Most importantly, the administration also feels that time is running out on the peace process, which is likely to die from inertia unless the United States makes a significant gesture to keep Hussein from becoming discouraged.

The problem has been building for a long time. Jordan has sought for years to rebuild its armed forces with American equipment, including fighter aircraft, tanks and a variety of ground-to-air missiles. Saudi Arabia, whose previous purchases of U.S. planes caused bruising congressional battles in 1978 and 1981, also has been anxious to acquire more F15s and other weaponry.

Congress, however, recalling the acrimony of those earlier fights, was reluctant to deal with new arms sales to the Arabs during the 1984 election year, particularly after Hussein in a fit of pique charged that Capitol Hill was under the sway of the Israeli lobby. Accordingly, the administration advised Hussein and King Fahd of Saudi Arabia to wait until the elections were over and Reagan had a mandate for a second term.

When Fahd visited here last February, some senior officials, led by Defense Secretary Caspar W. Weinberger, argued that Reagan should use the occasion to move on the Saudi sale. However, the revelation that this idea was under consideration provoked a new uproar in Congress and forced the administration to temporize again by declaring a moratorium on all new Mideast arms sales while a study was undertaken of the defense needs of the countries in the region.

Also in February, a new factor entered the equation when Hussein and Palestine Liberation Organization Chairman Yasser Arafat agreed on a proposal that the United States meet with a Jordanian-Palestinian delegation as a possible prelude to negotiating with Israel.

Following a period of exploration that included trips to the Middle East by Shultz and Murphy, the administration concluded that the idea might provide the key to reviving Reagan's stalled 1983 Mideast peace initiative. In deference to Israel, the United States ruled out participation by PLO members in the proposed delegation, while specifying that any meeting must show promise of direct talks with the Israelis.

By the time Hussein visited Washington at the end of May, U.S. hopes had risen so high that Reagan persuaded the king to appear before reporters on the White House lawn to express their joint hope of peace talks by year's end.

Despite a new trip by Murphy to the region last month, however, the hoped-for meeting with a joint delegation has still not materialized because of failure to agree on a list of Palestinian participants and Hussein's refusal to commit himself to eventual talks with Israel.

Inevitably, the search for a way to the bargaining table has become bound up with the arms sales. The administration, in addition to arguing that Hussein has legitimate defense needs, also contends that providing him with arms would induce him to negotiate with Israel. Similarly, the Saudi sale is seen as a way of showing U.S. evenhandedness to the Arab world while swinging Saudi support behind Hussein.

In June, the administration tested congressional sentiment on the Jordan sale, but was forced to retreat after Lugar and Senate Majority Leader Robert J. Dole (R-Kan.) warned that the plan had no chance. Congress did vote $250 million in economic aid for Jordan, but it also specifically barred sale of advanced weapons unless Reagan certifies to Congress that Hussein is "publicly committed to the recognition of Israel and to negotiate promptly and directly with Israel."

In his meeting with the House panel Tuesday, Murphy reportedly conceded that the administration is unable do make such a certification now. That provoked warnings that Congress is unlikely to finance the Jordanian sale and also will try to block the Saudi package, even though the Saudis can pay cash and do not require U.S. credits.

The administration has not indicated whether it has any strategy for overcoming that sentiment other than through intense lobbying. Hussein, Egyptian President Hosni Mubarak and Israeli Foreign Minister Shamir are expected in New York at the end of the month for the U.N. General Assembly meeting, and it is possible they will visit Washington. But whether Hussein and the administration will be able to agree on some new step that might change the mood of Congress is far from clear.