President Reagan yesterday committed himself in general terms to a new "build-down" approach for U.S. strategic nuclear arms control proposals, in which more atomic warheads would be destroyed than deployed in the future by both superpowers.

After pledging to senators that he would pursue this approach actively, Reagan promptly won another congressional vote releasing money for the controversial MX intercontinental ballistics missile that Congress blocked last year.

The Senate Appropriations Committee voted, 17 to 11, to approve $625 million for the MX. This includes $560 million for engineering and $65 million for flight testing the mammoth missile, which will carry 10 nuclear warheads.

A House Appropriations subcommittee also gave the green light to the MX Wednesday after Reagan sent House members a letter pledging flexibility in nuclear arms control negotiations with the Soviet Union.

In a similar letter yesterday to Sens. Sam Nunn (D-Ga.), William S. Cohen (R-Maine) and Charles H. Percy (R-Ill.), Reagan committed himself to the build-down approach, but was vague about how it will be incorporated into revised U.S. proposals when the strategic arms reduction talks (START) resume at Geneva next month. However, all three senators praised the president's letter.

"We are satisfied the president has endorsed build-down as part of arms negotiations with the Soviets," Nunn said in a hallway news conference before the Senate Appropriations Committee voted. He added that he intends to follow the progress of the arms control negotiations to make certain the new proposal was incorporated into the U.S. position.

The endorsement of build-down was the latest in a series of moves made by the administration to win approval of a package recommended by the President's Commission on Strategic Forces that includes deploying 100 MX missiles in existing silos and speeding development of a new, single-warhead missile that would be a less inviting a target than the MX.

At the White House, communications director David R. Gergen said Reagan was "extraordinary pleased" with the action of the Senate committee, considered one of the most difficult hurdles faced by the administration in its effort to win congressional endorsement of the MX after two earlier rejections.

Another senior official called Reagan's endorsement of build-down "a milestone," and insisted repeatedly to reporters during a briefing that the president's action was a real change in position rather than simply a political device to gain MX support.

The build-down endorsement is "not a cover for us to build rather than to reduce," the official added.

Reagan's letter to the senators, however, stopped far short of endorsing the original build-down proposal enunciated by Cohen and Nunn, in which two older nuclear weapons would be retired for each new weapon deployed.

The president's letter discussed using "variable ratios as appropriate," and the senior White House official said this meant that different ratios might be used for different weapons systems. The goal, he said, would be to "balance equality and stability" in the process of arms reduction so neither side would gain an advantage while reducing nuclear arsenals.

Cohen said that in some cases this could mean a ratio in which as many as three warheads are removed for each new one deployed. In other cases, however, the ratio could be little more than one warhead removed for each new one deployed.

The Senate Appropriations Committee vote yesterday reflected the political effectiveness of the bipartisan approach the White House has been stressing to build support for the MX package. Twelve of the 15 Republicans on the committee voted for the measure, but the margin of victory was provided by five Democratic senators.

Making an appeal that the president needed the MX as a bargaining lever in arms control negotiations with the Soviets, Sen. John C. Stennis (Miss.), the ranking committee Democrat, said: "I can't conceive of not giving him what he's asking for. It would be a grave mistake in the world of diplomacy."

Last year, the same committee voted 16 to 12 against the MX, but a principal point of objection then was the administration's advocacy of a "Dense Pack" basing system that the White House has since abandoned.

MX opponents yesterday focused on the vulnerability of the missiles to Soviet attack. The presidential commission, headed by Brent Scowcroft, acknowledged this vulnerability, but said that the system as a whole was not vulnerable because the Soviets would be unable to simultaneously destroy the MX, submarine-based missiles and missile-carrying bombers.

Sen. Dale Bumpers (D-Ark.), who voted against the MX funding, said yesterday during the debate that "the Soviet Union won't even have to retarget their missiles if the MX is stuffied into existing Minuteman silos." His alternative was to upgrade the Minuteman force.

Administration strategists were hopeful last night that the back-to-back votes of the two congressional panels would build an irrestible momentum for the MX that would result in decisive approval in both houses. Even before the Senate committee vote, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) conceded that momentum was building.

"Ten days ago . . . I thought the MX would be eliminated by 75 votes. I thought the MX was dead," O'Neill said. "I think it's a waste of money, to be perfectly truthful, but chances are we'll go along with it."

Like others on both sides of the issue, O'Neill credited the president's letters to undecided members of Congress with tipping the balance.

On Wednesday, before a vote in the House Appropriations subcommittee on defense, Reagan wrote Rep. Norman D. Dicks (D-Wash.) and eight other undecided Democrats that he would pursue arms reduction as vigorously as he has deployment of the MX.

Reagan also said he saw "merit in a panel with bipartisan composition and with staggered terms of membership to provide advice and continutity" in arms control, a statement he repeated yesterday in his letter to the three senators.

The House subcommittee voted 9 to 3 for MX funding, compared with a 7-to-5 vote of approval last year before the House subsequently voted down the president's proposal.