The General Services Administration, striving to persuade federal agencies to give up millions of dollars worth of office space, got some additional muscle this week in the form of a presidential order.

An executive order, signed Tuesday by President Reagan, gives the GSA new authority to enforce its space-reduction regulations in agencies that traditionally have managed much of their own space, such as the Defense Department and the Veterans Administration.

"We got exactly what we wanted," GSA Administrator Gerald P. Carmen said yesterday.

The GSA is trying to get federal agencies to reduce the average amount of space allotted to an employe from 166 square feet to 135, partly to parlay a smaller federal work force into a double savings: fewer people on the payroll and smaller bills for leased space.

Since August, 1982, GSA officials have visited 75 agency offices throughout the region and have recommended that agencies give up $5.3 million worth of rental space.

Agencies pay rent to the GSA for both leased and government-owned space. The GSA in turn acts as the leasing agent for most of the government's civilian agencies.

So far the GSA has recovered $342,671 worth of office space and agencies have agreed to give up another $1.4 million worth. Under new space management regulations, the GSA is charged with pressing its tenant agencies into 10 percent less space by the end of fiscal 1984. Agencies already at 135 square feet per person or less are exempt.

But it hasn't exactly been easy.

"Agencies measured their power by the amount of space they had," said James G. Whitlock, GSA's assistant regional commissioner of public buildings. "But space is no longer a status symbol unto itself. In the past, if a manager's office was the size of a basketball court, then he had clout."

GSA officials say agency officials aren't expressing any fears that federal workers will end up jammed together, elbows interlocked. According to Carmen, many major commercial firms assign their employes 120 to 130 square feet of space.

But managers for seven local agency offices said efforts to trim space were both out of line and out of the question.

In the past, agencies were able to fend off the GSA's questions about their space by citing their need for the space without additional justification, said William B. Jenkins, GSA regional realty chief.

Under the new federal regulation, agencies will have to submit a plan by May 15 on how they intend to get down to the average of 135 square feet nationwide.

But the kicking and screaming continues.

Raymond F. Wisniewski, associate director for administration for the Selective Service System, refused to give up 2,475 square feet of space in the agency's national headquarters building in Georgetown.

"Security is our foremost concern," Wisniewski said. "This agency has a controversial mission in support of national defense and as an example several hundred people were demonstrating outside our headquarters building last week."

The GSA's space utilization director, Kenneth L. Perrin, said the GSA backed off. "What else could we do?" he asked.