President Reagan, lobbying hard for approval of the MX missile, told members of the House Appropriations Committee yesterday that he was willing to give written assurances of his commitment to arms control.

At the same time he denounced the much-amended and watered-down version of the nuclear freeze resolution passed by the House on Wednesday, and said he was confident that if the resolution is debated in the Senate "the doubts and opposition to a simple freeze . . . will continue to grow."

In a White House meeting before he departed on a five-day, campaign-style trip, Reagan told the members of Congress that the MX is needed to prod the Soviets to negotiate an arms control agreement. He also said the administration is studying a proposal contained in letters sent him earlier this week by key members of both houses to set up a permanent bipartisan arms control advisory commission.

"This proposal is under active consideration," said a White House official. "The president's looking at it and he's open to it."

Moderates in both parties in Congress have indicated that they want some assurance of Reagan's commitment to arms control before they will vote for the MX. Reagan's response yesterday won cautious endorsement from two of the House members who signed this week's letter.

It urged Reagan to take specific steps to show that he is as fully committed to the arms control recommendations of his advisory Commission on Strategic Forces, headed by Brent Scowcroft, as he is to the commission's recommendation for deployment of 100 MX intercontinental ballistic missiles.

Reagan set up the commission to find some politically acceptable basing plan for the MX. It made its recommendations earlier this year.

Rep. Norman Dicks (D-Wash.) said, "If the president gives the kind of assurances we've asked for he's got a very good chance" of winning approval of the MX.

Rep. Vic Fazio (D-Calif.) called the president's statement to the congressmen "the beginning of reassurance to moderate Republicans and open-minded Democrats that he is fully committed to the entire Scowcroft commission report rather than just using it to win approval of the MX."

He said that presidential agreement to an advisory commission, first suggested by Sen. Sam Nunn (D-Ga.), would be an important step in the direction of "establishing the kind of bipartisan consensus that existed during the 1960s."

Fazio suggested that continuity between administrations could be achieved either by having staggered fixed terms for members or by allowing Congress to share the appointing responsibility.

Sen. Henry M. Jackson (D-Wash.), who met with Reagan on an unrelated matter, said the commission idea "had promise," and also predicted congressional approval of the MX, which he supports. However, administration officials acknowledged that they are still a few votes short in the House, and agreed with Dicks and Fazio that Reagan's response on arms control was likely to determine the outcome.

The president responded to House approval of a "mutual and verifiable freeze" on nuclear weapons with a written statement issued by his press office that called the resolution "ambiguous and indeed so internally inconsistent that interpretation is difficult."

"The resolution finally adopted by the House, while greatly improved, is not an answer to arms control that I can reasonably support," Reagan said.

On Capitol Hill, Secretary of Defense Caspar W. Weinberger also spoke out against the freeze, saying, "We don't want to freeze when we are behind."

Testifying before the Senate Appropriations Committee, Weinberger ran into open skepticism from members who contended that nothing would be gained by spending $16.6 billion to place MX missiles in existing Minuteman silos which the Scowcroft commission acknowledged would be vulnerable to Soviet nuclear warheads.

Responding to this concern, Weinberger put renewed emphasis on a $450 million Pentagon research program aimed at finding some way of "superhardening" the silos. He said that "hardening may well add to survivability" and argued that, in any case, the MX missiles will be "very much less vulnerable" than the Minuteman III missiles they will replace.