President Reagan won a partial victory in his fight for increased military aid to El Salvador yesterday as a Senate Appropriations subcommittee agreed to give him an instant $60 million he had requested.

But the Senate subcommittee also attached some conditions to the aid, and members of two other panels that must also pass on the request--the Senate Foreign Relations Committee and House Appropriations subcommittee on foreign operations--predicted last night that there would be sharp cuts. The House subcommittee postponed its vote until after Easter.

In a three-page letter to Secretary of State George P. Shultz, seven of the nine members of the Senate Appropriations subcommittee on foreign operations agreed to let the administration shift the $60 million from other countries to El Salvador if it will agree in writing to limit the number of U.S. military advisers and trainers in El Salvador to 55, encourage Salvadoran judicial reforms and make an effort to bring about unconditional discussions between the Salvadoran government and rebels there.

Two subcommittee members, Sens. Mark O. Hatfield (R-Ore.) and Patrick J. Leahy (D-Vt.), refused to sign the letter of approval on grounds that the aid is too high and conditions are too few. A third member, Sen. Daniel K. Inouye (D-Hawaii), signed "with reservations" for similar reasons.

The administration lobbied hard for its controversial request in the subcommittee, whose chairman is Sen. Robert W. Kasten Jr. (R-Wis.). Reagan telephoned at least one member, Sen. Arlen Specter (R-Pa.), and Shultz shuttled between House and Senate all day Tuesday, then was on the telephone with Kasten late Tuesday night on the terms of the compromise.

Assistant Secretary of State Thomas O. Enders and Undersecretary William Schneider holed up in a room off the floor until past midnight as Kasten tried out different versions of the conditions.

"We were bleary-eyed," Kasten said. "They wanted further refinements, but I was out of wiggle room. I just told them no."

Kasten said the administration achieved "a modified victory because they get the full amount of military aid, but we put them on notice we wanted action in specific areas." Administration officials said last night they expected to comply with the conditions and did not expect them to lead to a change in U.S. policy. However, they were unhappy with the limit of 55 trainers because, if the aid amount is ultimately cut, it would be cheaper to train more soldiers in El Salvador than bring them to the United States.

The are also uncomfortable with the wording on "unconditional discussions" which calls for talks, not only on rules for the upcoming Salvadoran elections, but also on "any other subject of concern between the parties." The administration has sought to limit any talks to the elections and how the leftists might safely participate.

On the Foreign Relations Committee, Chairman Charles H. Percy (R-Ill.) called a meeting yesterday morning to propose cutting back the aid request to $35 million without future conditions. He withdrew his proposal after objections from Sen. Christopher J. Dodd (D-Conn.).

Dodd and Sen. Nancy Landon Kassebaum (R-Kan.) have won over a number of committee members to a plan to cut the aid to $23.7 million and hold back further funds until there is progress toward unconditional talks between the Salvadoran government and guerrillas.

Later in the day Dodd amended this proposal to provide $30 million and impose conditions on future funds. These, in addition to requiring progress toward unconditional talks, would limit military trainers in El Salvador to 55 and put restrictions on any training outside El Salvador.

The House subcommittee deferred its decision after two days of hearings and closed-door discussions because of an illness in the family of Rep. Mickey Edwards (R-Okla.).

Chairman Clarence D. Long (D-Md.) said it was essential to have all members present at the vote, and told Enders that if the administration would not agree to a delay the committee would simply deny the funds. Under normal procedures the administration could reprogram the money on Friday if no governing committee objected before then.

After a caucus of subcommittee Democrats, Reps. David R. Obey (D-Wis.) and Matthew F. McHugh (D-N.Y) predicted that the subcommittee would give the administration less than half of what it has asked for, and that further aid would be conditioned both on progress toward unconditional talks with the rebels and on human rights progress.

But exactly what the subcommittee will do remained unclear last night.