President Reagan tried to convince wavering Republican House members yesterday that they will "unilaterally weaken" the U.S. bargaining position at the forthcoming Geneva arms control negotiations with the Soviets if they fail to approve funds for building additional MX missiles.

"I want to impress upon you my seriousness of purpose in pursuing a meaningful arms-reduction agreement and ultimately the elimination of these weapons," Reagan said in a statement he read to a group of 30 Republican members of Congress. "I would like nothing better than to be able to eliminate these weapons for future generations and to reduce the cost of our national defense by reducing these weapons."

The president's argument was calculated to appeal to Republicans who have balked at administration defense budget requests. Reagan is seeking to persuade Congress to release $1.5 billion appropriated last year for production of 21 additional MX missiles, which he calls the Peacekeeper.

The vote has been timed by the administration to come within a week of resumption of the arms control talks, and Reagan's major contention has been that a negative vote on the MX would undermine the U.S. negotiating position. Reagan told the House members that "there is no doubt the Soviet Union and other nations will be keenly following these votes to determine if we have the will to continue with our modernization program or if we will blink and unilaterally reduce our capability . . . ."

In his lobbying yesterday, Reagan also contended that the MX, if it helps obtain a new arms control agreement, could lead to reduced defense costs.

Slightly more than 12 percent of the defense budget is spent on strategic weapons, and only a fraction of this is likely to be reduced by any arms control agreement. But a White House official said that even a small cutback would be significant in light of the deficit-reduction plans being considered by Congress.

The administration is now optimistic about prospects for the MX in the Democratic-controlled House. Rep. Dick Cheney (R-Wyo.), a member of the Republican leadership and a staunch MX supporter, said "we're making progress in the House" and added that "the only way a member can vote against the missile is if he substitutes his judgment for the president's that this will help us negotiate arms control at Geneva."

But administration officials expect a more difficult battle in the Republican-controlled Senate. With this in mind, Reagan conferred yesterday with Senate Majority Leader Robert J. Dole (R-Kan.), and a spokesman said the president will meet with senators every day this week to lobby for the MX.

Congress previously approved deployment of 21 MX missiles, and Reagan is seeking 48 more of the 10-warhead missiles, at a cost of $4 billion, in his fiscal 1986 budget proposal.

Ultimately, the administration intends to deploy 100 MX missiles in existing Minuteman silos, which will be "hardened" for better protection but which officials acknowledge will be vulnerable nonetheless.