The Carter Administration, anxious to avert a controversy with major foreign-policy implications, hopes to convince Saudi Arabia to defer for the time being its request for improvements in the combat capability of its U.S.-supplied F15 fighters.

Reliable sources said yesterday the administration is evolving a strategy aimed at persuading the Saudi government that neither country's interests would be served by forcing the issue to a decision at this time.

Instead, the sources said, the United States will argue that any attempt to satisfy the Saudi request in the current U.S. political climate would provoke a battle with Congress that is likely to result in the Saudis being denied the equipment and armaments that they want for their jet planes.

At the same time, the sources added, the administration will seek to make clear that postponing a decision should not be interpreted by the Saudis as a backdoor rejection of their request.

President Carter, they said, has not yet decided what to do about the Saudi demands. But, the sources continued, if he is allowed a breathing space of an additional few months, the administration will be in a much better position to pursue the political horse-trading and educating of U.S. public opinion that would permit at least a partial satisfaction of the Saudi desires.

The sources admitted that the adminstration still does not know whether this attempt to buy time will work, especially since Saudi leaders are understood to have informed Washington that failure to provide the equipment could seriously damage U.S. relations with its principal oil supplier and ally in the Persian Gulf region.

Specifically, the Saudis have asked for missiles, extra fuel tanks and bomb racks that would significantly enhance the range and firepower of the 60 F15s that the United States is supplying to the Saudi Air Force. The F15 is the most advanced aircraft in the U.S. arsenal, and the administration's 1978 decision to make it available to Saudi Arabia provoked major opposition from Israel and its American supporters.

According to U.S. officials, the improvements being sought by the Saudis would extend the plane's range from 450 miles to more than 1,000 miles, giving it the ability to attack Israel.

Despite that fact, influential national security officials within the administration are understood to have supported the Saudi request initially on the grounds that the United States cannot afford to offend the pride and power of so important an ally, particularly at a time when U.S. policy puts a major premium on strengthening resistance to Soviet influence in the area.

However, the sources said, that initial tilt since has been eroded by what one called "a firestorm of opposition" building up in Congress. Under the law, any foreign military sales of $25 million or more can be blocked if Congress votes against it.

Currently, the sources continued, the opposition on Capitol Hill appears so intense that administration vote counters frankly are doubtful that Carter could beat back a congressional move to derail sale of the additional equipment to Saudi Arabia.

The congressional hostility comes not only from traditional supporters of Israel and other members of Congress, concerned about the Jewish vote in an election year, but also from a large number of other influential members who regard the Saudi request as a breach of the understandings under which Congress originally agreed to the sale of the F15s.

In May 1978, as part of the adminstration's campaign to put the sale across. Defense Secretary Harold Brown wrote to the Senate Foreign Relations Committee, saying: "Saudi Arabia has not requested nor do we intend to sell any other systems or armaments that would increase the range or enhance the ground attack capabilities of the F15."

During the past few days, the White House has received a barrage of congressional reminders of that promise. Typical was a letter sent to Carter Thursday by six influential senators that said bluntly:

"We hope that you will clarify to the Saudi government the nature of the agreement reached during Senate consideration of this matter, and reject without delay their request for aircraft modifications."

That, the sources said, is the reason the administration has decided that its most prudent course is to try and buy time -- possibly until after the November elections -- by appealing to the Saudis for patience. But, the sources added, in pursuing that course, the administration, mindful of Saudi sensibilities, plans to feel its way through slow and measured moves rather than make an abrupt plea for a postponement.

For example, Brown will meet the Saudi defense minister, Prince Sultan, in Geneva next Thursday. But, as one source put it, "It's doubtful that he'll make a direct approach for a temporary shelving of the Saudi request. Instead, it's much more likely that they'll talk around the matter, with the United States trying to get its point across by asking for 'clarifications' and other ways of hinting at delay."

The sources said this indirect, feeling-out process is likely to continue until the Saudis make clear whether they are willing to cooperate by waiting. In the meantime, they added, the administration will miss no opportunity to reinforce subtly but unmistakably that the Saudis stand a much better chance of getting what they want by being patient.