The Smithsonian Institution and the National Gallery of Art will drastically cut back and in most cases eliminate extended summer hours at Mall museums this year, evening hours that have been available to area residents and tourists for much of the past two decades.

Officials at both institutions blamed the cutbacks on federal budget reductions, what one spokesman described as a "pattern of general stringency."

In past years, Air and Space, the most heavily attended of the Smithsonian museums, has remained open until 9 p.m., and the four other Mall museums -- American History, Natural History, the Hirshhorn and the Castle, had been open until 7:30 p.m. during the summer. The new plans call for Air and Space to remain open until 7:30, while the other Mall museums will close at 5:30.

The National Gallery of Art, which in the past has remained open until 9 p.m. on summer evenings, will close at 5 p.m. this summer. The museum's regular Sunday evening hours will remain unchanged.

According to spokesmen for both the National Gallery and the Smithsonian, the change in hours is a direct result of a 2 percent cut in this year's federal budgets for both institutions. Unexpected utility expenses as well as salary costs also contributed to what officials describe as a budget crunch.

The Smithsonian cut back its schedule similarly in 1982 but had restored the hours entirely by last summer.

Although both institutions' multimillion-dollar budgets are paid out of tax dollars, spokesmen for both the National Gallery and the Smithsonian said they had no choice but to reduce public access to their collections.

"We're not striking out at the public," said John F. Jameson, assistant secretary for administration at the Smithsonian. "Every sector of the operation is cutting back."

The Smithsonian has requested money in its 1986 budget to restore evening hours, Jameson said, but there is no way to tell whether sufficient funds will be appropriated. "It's very difficult for us to predict how the Institution will fare," Jameson said.

Spokesmen at both the Smithsonian and the National Gallery said that although both institutions have large budgets there is less flexibility than might be imagined because much of the money is earmarked for specific purposes.

The Smithsonian's Quadrangle, for example, a $75 million project on the Mall designed to house museums of Asian and African art, is paid for out of funds set aside for construction only, according to the Smithsonian.

Money for extended summer operations, the costs of which are largely for utilities and security, are paid out of operating funds. "There isn't that much maneuvering room," said National Gallery Administrator Joseph G. English.

An estimated 2 million people visit Smithsonian museums on the Mall each year during extended evening hours, Jameson said, describing the change as a regrettable necessity. "I think we're in the business of public service, and in that sense we are not serving our purpose. Certainly we're not happy about that."

Smithsonian spokesman Al Rosenfeld said yesterday that he did not know whether the change in hours had been formally approved by the Institution's Board of Regents, but that the regents "were certainly aware of the change and did not reject it."

Keeping the National Gallery open summer evenings costs approximately $350,000, according to English -- money that could not be found elsewhere in the budget. "There's really no other place we could take it from," English said. "We've had to search every nook and cranny, we've had to skip one window washing, we're even looking at $100 and $200 items and that still leaves us short on normal functions."

English estimated the number of evening visitors to the gallery during the course of the summer at "not more than 10,000. I can remember nights where we had only 200 or 300 people." He added that he could not be sure when or if evening hours at the Natural Gallery would be restored.