The Defense Department yesterday moved immediately to recover the $124 million that it said Thursday it had overpaid General Dynamics Corp. for overhead expenses in the past 12 years.

It announced that it will deduct the amount from the giant defense contractor's current billings for production of major weapons system.

At the same time, the Pentagon said it will continue to freeze $30 million in monthly overhead payments until the company reforms billing procedures to prevent frivolous claims.

The moves came a day after Pentagon auditors concluded that General Dynamics had been paid $244 million more than it should have for overhead costs since 1973. Of the overpayments, the Pentagon said it previously had recovered $120 million through normal accounting procedures.

Auditors were ordered to review past overhead billings last month after General Dynamics officials admitted improperly charging the government for personal entertainment, travel and kennel fees for a corporate executive's dog.

Those admissions to a congressional committee fueled efforts on Capitol Hill to cut the Reagan administration's $313 billion defense budget proposal for fiscal 1986 and gave Pentagon critics evidence of lax Pentagon management.

In yesterday's announcement, the Defense Department said it will recover the remaining overpayments by withholding $124 million from the company's monthly billings for labor and material used in weapons production.

General Dynamics, the nation's largest defense contractor, receives about $700 million every month from the Pentagon in "progress payments" to cover the costs of building weapons. Only years later does the Pentagon audit the accounts of defense contractors to ensure that their claims were in line with procurement rules.

Rather than waiting for General Dynamics to reimburse the balance of the overpayments -- a possibly lengthy process that might further incite congressional critics -- the Pentagon now plans simply to pay the contractor about $576 million for its next billing.

"We want to get the money as soon as possible," a defense official explained. "If we withhold the payments, we make sure the money is in the federal treasury, not company coffers."

Of General Dynamics' monthly payments, $30 million is earmarked for overhead expenses, a loosely defined category of "general and administrative" costs related to weapons production. Recent reports have shown that contractors have interpreted overhead to include political contributions, promotional gifts and lobbying.

When Defense Secretary Caspar W. Weinberger announced the General Dynamics audit March 5 as the spearhead of a "get-tough" policy against defense contractors, he froze the firm's overhead payments.

In the move announced yesterday, the Pentagon said it will continue the suspension of overhead payments until General Dynamics changes accounting and management practices to prevent billings for expenses unrelated to weapons production.

Since auditors are unable to monitor billings for years because of their sheer number, they count on contractors to submit honest claims.

General Dynamics has recently submitted for Defense Department review a list of accounting changes designed to identify and separate frivolous overhead claims from those allowed by federal acquisition rules, according to a Pentagon statement.

To encourage honest claims, Weinberger began requiring contractors last month to certify that their overhead claims are allowable. Corporate officials who knowingly submit phony claims can be prosecuted for perjury.

The excess overhead payments to General Dynamics resulted from its improper billings for workmen's compensation, use of company computers, corporate acquisitions and plant "rearrangements," according to the statement. There were no details.

In addition to General Dynamics, Pentagon auditors are examining past billings and billing procedures of the 30 top defense contractors, amid congressional concern that improper claims are endemic to the industry.

Weinberger has said he believes the abuse is limited to "a few bad apples."