The Reagan administration yesterday sought to reassure a worried Congress that the president is as firmly committed to arms control as he is to deployment of the MX missile.

"The president's commitment to arms reduction is complete and absolute," said Secretary of Defense Caspar W. Weinberger in a statement responding to two bipartisan congressional letters calling upon Reagan to endorse the arms control recommendations of the President's Commission on Strategic Forces.

Weinberger told a congressional subcommittee that Reagan supports all of the recommendations.

The report of the bipartisan commission calls for deploying 100 MX intercontinental ballistic missiles in existing Minuteman silos in Wyoming and Nebraska and development of a small single-warhead missile that would be a less tempting target than the MX.

The Air Force announced yesterday that it is opening a Small Missile Program Office at Norton Air Force Base, Calif., to manage development of the new 15-ton missile, often referred to as "Midgetman."

Reagan has strongly favored both the MX and the small missile, which would be ready for full-scale development by 1987 and deployment in the 1990s.

But some congressional critics have expressed concern that the president is not nearly as enthusiastic about another commission recommendation that calls for the counting of warheads, rather than missile launchers, in arms control negotiations with the Soviet Union. A letter sent to the president this week by Senate Foreign Relations Committee Chairman Charles H. Percy (R-Ill.) and co-signed by Sens. William S. Cohen (R-Maine) and Sam Nunn (D-Ga.) called on Reagan to amend the U.S. proposals at the strategic arms reduction talks (START) in Geneva to count warheads.

The letter also sought U.S. advocacy of a "build-down" proposal in which two nuclear missiles would be destroyed for each one deployed. "I think we're going to get a favorable response," Percy told reporters after a meeting at the White House with the president. "He didn't give it right there, but they're giving very serious consideration to it."

Administration officials said later in the day that a letter would be sent by the president to the three senators and to a group of House members who wrote a similar letter assuring them that he fully endorses the commission's arms control recommendations.

However, one administration source acknowledged that the president would like to be "unspecific, for the time being" about the "build-down" proposal. This source said that the administration was concerned with "the practicality of the idea rather than the concept."

White House spokesman Larry Speakes said the letter by Percy and his colleagues reflects "the bipartisan spirit needed to achieve our goals" but did not specifically endorse the letter's requests.

Speakes' deputy, Lyndon Allin, hinted that the administration was still some distance from formally changing its position. "Now if we're going to move to single warheads and the Soviets do the same, then that is going to necessitate a change in how we discuss these proposals in Geneva," Allin said. "But this is all under review and I think it would be a little bit premature to start saying exactly what's going to happen in the package."

There has been no indication from the Soviets, who have been building multiple-warhead missiles, that they would favor a single-warhead approach.

The 100-ton MX missile would have 10 warheads. The Air Force yesterday said it would seek $600 million for developing the small missile, which could be mobile or based in silos.