President Reagan indicated yesterday that he does not necessarily feel bound by the Senate Foreign Relations Committee's Thursday vote to halve his request for $60 million in added military aid to El Salvador.

"Well, fortunately they don't have to do with appropriations," Reagan told a group of students by telephone from the White House. "That was a non-binding type of thing which they recommended, cutting the aid to El Salvador. Incidentally, that was a very close vote in there, but the Appropriations Committee has already, they have recommended to the floor the increase in spending that we had asked."

Lyndon K. Allin, deputy press secretary to the president, said the administration plans to work with all the committees in Congress that have an interest in El Salvador, and the Foreign Relations Committee's recommendation for the aid package is but one of those views.

"We haven't got the whole process completed," said Allin. "The House vote is still to come. We won't take any position until all the committees are done and we can develop a consensus. We are still asking for $60 million."

Allin said that by precedent it is the Appropriations committees, not the Foreign Relations Committee, that determines the amount of foreign aid packages, and only a 1981 letter entitles the Foreign Relations Committee to make known its views on the appropriations.

Reagan also told the students that he may favor a study of the Social Security system to see if it should be reshaped. He said, "I don't think there would be anything wrong if we had some solid studies made as to whether we could improve the program for all of you so that it would be more fair for you and for the younger workers in the work force today and in the future."

Trying to regain the political momentum after a Democratic budget proposal won House approval Wednesday, Reagan said that his economic policies are a success and that Democratic attempts to raise taxes risk killing an economic recovery that has "definitely" begun.

The president began a 15-minute news conference by offering an olive branch to the opposition party. He thanked Democratic and Republican legislators alike for "working together in our best bipartisan tradition" to pass a bill early yesterday morning to rescue the Social Security system from insolvency.

And he later reiterated his willingness to work with congressional Democrats, who are beginning to show the strength of the increased numbers they gained in the November election, by saying he was "gratified that good sense did prevail over partisan concerns" to get the jobs legislation passed. "I'm asking all members of the Congress to work with me to hold down spending and taxes in the same bipartisan spirit that's brought us such great progress on jobs and Social Security," Reagan told reporters two days after House Democrats approved a budget calling for smaller increases in defense spending and more spending on social programs than he wanted.