WASHINGTON — After an unanticipated response from car owners seeking new car discounts under the “cash for clunkers” program, the government was reported Thursday evening to have exhausted the funds available, leaving unclear whether further applications would be accepted.

The National Automobile Dealers Association surveyed its members and told the Transportation Department that it had a very large backlog of applications, according to Bailey Wood, a spokesman for the association. Late in the day the group said the Transportation Department had responded by telling it to stop taking applications at midnight.

But the Transportation Department and the White House would not immediately confirm that the program had been halted.

About a quarter-million vehicles were sold under the program, which offered payments of $3,500 to $4,500 for people who traded in old cars for new ones that had higher fuel economy. The average payment worked out to about $4,000, and the total payout, about $1 billion, the amount allocated by Congress under the program, formally called the Car Allowance Rebate System, or CARS.

A statement issued Thursday evening by the White House said: “We are working tonight to assess the situation facing what is obviously an incredibly popular program. Auto dealers and consumers should have confidence that all valid CARS transactions that have taken place to date will be honored.”

Wood said that his group would ask Congress and the White House to add money to the plan.

The sudden depletion of the fund was a surprise.

On Thursday evening, the government Web site describing the program, http://www.cars.gov/, still showed a chart shaped like a fuel gauge that indicated $779 million was available for trade-ins of cars and light trucks. Earlier Thursday, the Transportation Department issued a news release that said that applications for fewer than 23,000 vehicles had been submitted as of Wednesday, with a rebate value of just under $100 million.

The Transportation Department had begun accepting applications on Monday, when rules putting the program in place took effect. But car dealers had been accumulating the applications since July 1, when Congress put the law into effect.

Congress evidently did not anticipate that the money would fly out the door so fast; it said that applications would have to be submitted by Nov. 1.

The program had two goals: aiding the ailing car industry, and improving fuel economy in the fleet on the road.

Cars submitted under the program were junked, not resold. They had to be less than 25 years old, and have a fuel economy, as rated by the window sticker, of 18 miles per gallon or less.

The size of the rebate depended on the fuel economy of the replacement vehicle. Consumers were also supposed to receive the scrap value of their trade-in.

From the dealer’s point of view, the program was a resounding success.

“Two hundred and fifty thousand vehicles in four weeks?” Wood said. “One word comes out of my mouth: Wow.”

As word spread unofficially on Thursday night, car dealers were suddenly plunged into confusion.

A Ford dealership in Paramus, N.J., did not know of the apparent suspension until a reporter called seeking comment.

Other dealers said they had no idea what the suspension meant or whether the deals that they had already signed would be honored by the government. Some said they were notified by e-mail message by fellow dealers.

The dealers’ association, however, had been warning that the money would go quickly.

Until the cash-for-clunkers program began, the auto industry had been on track for annual sales of about 10 million units, down from the peak of about 16 million units a year.