More than two-thirds of the members of the U.S. Senate have signed a letter to President Carter urging him not to sell Saudi Arabia the extra equipment it wants to beef up the range and firepower for its U.S.-built F15 fighter planes.

The letter, sponsored by a bipartisan group of 14 senators, is certain to add fuel to a politically explosive controversy the administration confronts as it tries to balance the demands of two important countries -- Israel and Saudi Arabia.

Two years ago, in an effort to shore up U.S. relations with this country's biggest oil supplier, the administration agreed to sell 60 F15s, the best new fighter in the U.S. arsenal, to the Saudis for $2.5 billion.

The sale was strongly opposed by Israel and its supporters in Congress. It was approved only after administration officials, including Defense Secretary Harold Brown, gave specific assurances in writing to Congress that "Saudi Arabis has not requested, nor do we intend to sell any other systems or armaments that could increase the range or enhance the ground attack capability of the F15."

Though the first of these new war-planes will not be delivered to the Saudis until this fall, the controversy escalated sharply last month when it became known that the Saudis wanted to buy special fuel tanks, bomb racks and aerial refueling capabilities for the aircraft -- those items that specifically had been ruled out previously.

These improvements would extend the plane's two-day range from 450 miles to more than 1,000 miles, giving it the ability to hit Israel.

The Saudi request immediately posed foreign policy quandary for the administration. Rejecting it would likely further alienate the royal family, while approving it was certain to cause a furor here, especially in Congress and among Jewish voters as the election approaches.

The administration has argued that much has changed in the two years since the original sale. The Saudis are concerned about the Soviet Union, not about Israel, officials argued, and need some show of U.S. support.

Since the F15 agreement, the shah or Iran has fallen and with him went Iran's "policeman" status in the Persian Gulf. Meanwhile, an unstable Iraq is making a bid to replace Iran, and the Soviets have invaded Afghanistan.

The Senate letter, signed by about 70 senators, makes clear that the president would not get congressional approval for any follow-up equipment sale. The situation also has added to Carter's problems in dealing with Congress, because the letter reflects annoyance that the administration would even consider such a sale after the previous assurances.

On June 26, Brown traveled to Geneva to meet with the Saudi defense minister, Prince Sultan. At that meeting, informed sources say, Brown said the administration agreed with the Saudi view that the threat in the region had intensified and that it would seriously consider the Saudi request.

But Brown explained the previous assurances given to Congress and said that the administration would have to go back to Capitol Hill if new measures were to be approved. Brown told the prince there were no immediate plans to go back to Congress and no White House decision on the request was in offing.

Sources say there was no confrontational quality to the meeting. The prince listened and appeared to accept Brown's explanation, though there is no confirmation of that, officials acknowledge. The Saudis, did not withdraw their request.

It is generally believed in government circles that the administration will not act either way on the request until after the election.