President Reagan gave written assurance to Congress yesterday of his flexibility on nuclear arms control and was rewarded with an important House subcommittee vote allowing in-flight testing of the controversial MX intercontinental missile.

Rep. Jack Edwards (R-Ala.), ranking Republican on the House Appropriations subcommittee on defense, offered the motion to release $560 million in research and development funds for the MX, which Congress had denied Reagan last December.

After it passed by a decisive 9-to-3 margin yesterday, Edwards said Reagan's new written declaration of readiness to modify his position on nuclear arms negotiations had been largely responsible for the margin of victory. In a letter to subcommittee member Norman D. Dicks (D-Wash.), Reagan spelled out his willingness to change the U.S. arms control proposals in the Strategic Arms Reduction Talks (START) at Geneva to conform with the recommendations of the President's Commission on Strategic Forces, headed by Brent Scowcroft.

Reagan also told Dicks and eight other House Democrats, in answering a letter they sent last week, that he saw "merit in a panel with bipartisan composition and with staggered terms of membership to provide advice and continuity" in developing arms control and weapons systems proposals.

The letter from the House Democrats, urging Reagan to commit himself as strongly to arms control as he has to deployment of the MX, called for creation of such a commission, as did another letter from three influential senators.

The president's written response made no mention of the "builddown" concept under which both the United States and the Soviet Union would destroy two older long-range nuclear weapons for each new one deployed. Administration officials said, however, that this issue would be addressed today in letters to members of the Senate Appropriations Committee before it votes on MX funding.

Sen. Warren B. Rudman (R-N.H.), a member of this committee who met privately with the president yesterday, said his vote would depend in part on Reagan's commitment to builddown. Rudman said he had been assured that he would receive a letter from Reagan responding to his concerns before today's vote. The builddown issue was prominently raised April 29 in a letter to the president from Sens. William S. Cohen (R-Maine) and Sam Nunn (D-Ga.), who also met with Reagan at the White House yesterday.

Administration officials told The Washington Post on Tuesday that Reagan was "strongly leaning" toward the builddown concept despite some reservations about how it could be incorporated into revised U.S. strategic arms reduction proposals that will be offered to the Soviets after the START talks reconvene in Geneva on June 8.

Asked about the builddown idea during a photo session at the White House yesterday, Reagan said he supports "the concept" but that it it was "not as simple as it sounds."

"But yes that's something we very definitely will look at," he added.

In his letter to Dicks, Reagan promised to review the administration's START proposals "with the intention of developing such modifications as are necesssary to reflect the commission's approach."

This would mean substituting the counting of warheads for counting missile launchers as a measurement of the nuclear arsenals of the two superpowers.

"I agree wholeheartedly with the essential theme of the Scowcroft commission's approach to arms control: the attainment of security at the lowest possible level of forces," the Reagan letter said.

The president also promised, as he has before, to undertake "a major effort" to develop a smaller, single-warhead missile that would be a less tempting target than the 10-warhead MX and also less threatening to the Soviet Union.

Rep. Vic Fazio (D-Calif.), one of the authors of the House letter called the president's response "a good place to start."

"I think the president has recognized that, politically at least, he has to move to the center to pick up the votes of those who think that arms control reductions are an integral part of national security strategy," Fazio said.

But Rep. Joseph P. Addabbo (D-N.Y.), chairman of the Appropriations subcommittee that approved funding for the MX yesterday, said "the fight has just begun" to defeat the administration's plans to deploy 100 MX missiles in existing Minuteman silos. He said the next round would come when the Pentagon's fiscal authorization bill reaches the floor, probably next week.

White House spokesman Larry Speakes said the president was "very pleased" with the vote in Addabbo's subcommittee yesterday. Last year, the same subcommittee voted 7 to 5 in favor of the MX, which was subsequently overturned by the full House.

The two congressmen who switched yesterday were Rep. Joseph M. McDade (R-Pa.) and Dicks. Addabbo said both "used the president's letter as a reason to vote for the resolution."

Dicks called Reagan's message "a very strong letter." Another signer of the letter to Reagan, Rep. Albert Gore Jr. (D-Tenn.), said the president would abide by the commitments he gave about arms negotiations in his response. "When the president gives his word, he can be believed," Gore said.

Edwards said one of the most influential points in the letter was Reagan's commitment to "vigorous research and development on the single-warhead missile," which has won strong backing in Congress.

But the administration faces a stiffer test today in the Senate Appropriations Committee. Officially, the White House is saying that vote is too close to call. Privately, administration sources said last night that the president can prevail if he gives the proper assurances in the letter to Rudman.

Under a congressional deadline set last year, Congress must vote on the issue by June 6, 45 days after Reagan made his recommendations for MX deployment.

In another development yesterday, Reagan sent Congress a report required by law in which he said he is "strongly committed to preventing nuclear proliferation."

"The United States made progress in its non-proliferation efforts in 1982, but there also were problems," the report said.

The president sent a cover letter with the report which continued his efforts to demonstrate a concern for arms control, part of an all-out administration campaign to convince Congress that Reagan is as serious about arms reduction as he is about deployment of the MX. Officials said the letter also was intended as a response to members who have criticized Reagan for efforts to relax the sale of nuclear materials to other nations.

"Preventing the spread of nuclear weapons is a longstanding and fundamental security objective," the letter said. "My administration is strongly committed to that goal and has actively pursued it. We are undertaking further efforts with key countries on the need for urgent movement to strengthen measures against nuclear proliferation."