Secretary of State George P. Shultz yesterday sent a letter to key Senate Democrats that he hopes will settle a bitter legal dispute over Senate review of the U.S.-Soviet treaty eliminating intermediate-range nuclear forces (INF), senior administration officials said.

The letter, delivered to Capitol Hill late last evening, essentially accepts the three principal demands made by Senate Majority Leader Robert C. Byrd (D-W.Va.) and Senate Armed Services Committee Chairman Sam Nunn (D-Ga.) last Friday, the officials said.

Congressional aides to several conservative Republican senators, who had blocked an earlier Shultz attempt at compromise, appealed unsuccessfully to the White House to hold up the letter until their senators read it, according to several officials.

Administration officials said Shultz obtained the approval of Senate Minority Whip Alan K. Simpson (R-Wyo.) before sending the letter to Nunn and Byrd.

Shultz's attempt at resolving the dispute grew out of his concern that it could impede early ratification of the popular INF treaty, which last week became the object of bitter Senate wrangling over the administration's controversial "broad" reading of the 1972 Antiballistic Missile (ABM) Treaty.

Nunn and Byrd were meeting on the INF treaty with French officials in Paris yesterday and could not be reached for comment on Shultz's letter.

But some congressional officials cautioned that even if Shultz's letter satisfied Nunn and Byrd, it still would not settle the underlying dispute over the administration's "broad" or permissive interpretation of the ABM Treaty.

Sen. Joseph R. Biden Jr. (Del.), the Foreign Relations Committee's second-ranking Democrat, has said the dispute can only be resolved by attaching a "reservation" to the INF Treaty affirming the Senate's power to make legally binding the testimony of executive branch officials during ratification hearings.

Such a reservation would effectively enact Shultz's new pledges into law, amounting to a lasting repudiation of the administration's position, advanced by State Department legal adviser Abraham D. Sofaer in 1985, that executive branch testimony on arms treaties may not reflect their true meaning.

Sofaer advanced the theory to explain the administration's "broad" reading of the ABM Treaty in the face of Senate testimony by Nixon administration officials at the time supporting a more traditional, or "narrow," reading.

Shultz's letter yesterday promised that "all INF testimony of executive branch officials within their authorized scope {will be} authoritative" and said the Senate need not "incorporate" executive branch testimony and written materials "in its resolution of ratification."

This latter concession appeared to reverse the administration's previous position that executive branch testimony supporting the "narrow" interpretation of the ABM Treaty was not authoritative because it was not specifically mentioned, or "incorporated," in the Senate's vote of approval.

Shultz's letter also said that "the Reagan administration will in no way depart from the {meaning of the} INF Treaty as we are presenting it to the Senate."

Nunn and Byrd, angry about the Reagan administration's rejection of the Nixon administration's ABM Treaty testimony 13 years after it occurred, had demanded a slightly different Shultz pledge that "a meaning for the {INF} treaty different from that presented to the Senate by the Reagan administration cannot be adopted without the approval of the Senate."