A congressional plan requiring motorists to leave their cars at home one day a week continued to pick up support yesterday, as a top Energy Department official warned that gasoline shortages would continue into next October and would reappear next summer.

David J. Bardin, head of the Energy Department's Economic Regulatory Administration, told a House hearing yesterday, "Leave your car home one day a week, and we'll get through [the gasoline shortage]."

Bardin stopped short of endorsing a plan now being drawn up by Rep. Toby Moffett (D-Conn.) and other House members that could require a $5 minimum on gasoline sale and prohibit motorists from driving one day each week.

White House domestic affairs chief Stuart E. Eizenstat has participated in discussions with House members developing the plan. He has given Moffett no commitment of support, House sources said, but is reported to be "warm to aspects" of the plan.

Bardin told a meeting of two House subcommittees that the gasoline shortage was the result of the Iranian revolution and a decrease in world crude oil production. He said the shortage would last through the current summer driving season and is likely to occur again next year.

He said motorists should drive 15 fewer miles each week and use car pools and public transportation. But he added, "Let's not all stay home. Let's not shut down the country."

Energy Secretary James Schlesinger said lon lines at California service stations can be eliminated by enforcing the 55 mph speed limit and relaxing strict pollution controls in the state.

California's Air Resources Board approved a relaxation in the state's air pollution standards, which one official said could mean a 5 percent increase in gasoline production. The relaxation will expire Oct. 1.

A committee of the Nevada legislature approved a resolution authorizing the state to spend up to $10 million to purchase gasoline on world markets to help prop up the state's sagging tourist industry.

The Pentagon said petroleum shortages that have caused long lines at gas stations around the country have also caused a cutback of up to 10 percent in supplies reaching the Army, Navy and Air Force.

The NAACP, concerned about the rising cost of gasoline, will urge the Carter administration to develop a "fuel stamp" program for poor people.

In Washington, Moffett said he will introduce his reduced driving plan early next week. "It's to avoid a California-style shootout at the gas pumps," he said.

Under his proposal, states would issue stickers denoting the day of the week the car would be left home. While features of the bill are still being worked out, it is likely to set a nationwide $5 minimum for gas purchases to prevent topping off gas tanks.

Such questions as what to do about multiple-car families and how to enforce the plan are not resolved.

An aide to Moffett stressed that the plan was not intended as a rationing proposal or a substitute for the standby rationing plan the president challenged Congress to come up with after his own standby rationing plan was defeated in the House.

While Democratic leaders, such as Speaker Thomas P. (Tip) O'Neill Jr., (Mass.) have not endorsed the proposal, they have encouraged Moffett to work on it.

Moffett also is concerned that enough gasoline be conserved so the country does not have a shortage of home heating fuel in the winter.

A caucus of all House Democrats is expected to act Tuesday on another Moffett proposal, to continue controls on oil prices until 1981, despite the president's intention to start decontrol June 1.

Moffett is optimistic about getting the Democrats' endorsement of the plan, and House Majority Whip John Brademas (D-Ind.) said he "wouldn't be surprised" if the Democrats endorsed it.

If they do, Moffett will attempt to attach a proposal continuing the controls to an energy bill in the House Commerce Committee. Brademas said the full House might approve the extension.

The Commerce Committee recently rejected such an extension on a tie vote.

Even if the House approves the extension, it is widely believed that the Senate would block it, thereby making the House vote mote symbolic than effective.

Brademas said extending oil price controls has become a popular idea because of the questions House members are getting from constituents about whether the current gas shortage is a contrivance of the oil companies, holding back oil in anticipation of price decontrol.

"Oil companies have not behaved responsibly," Brademas said. "Even as reports of their gigantic profits are coming out, they have not made much effort to respond to the deep and wide concern that they look for more petroleum."