Red hot auto sales under the U.S. government's cash for clunkers incentive began to cool as dealer inventories tightened and showroom traffic showed signs of leveling off from its frantic pace of a week ago.

One industry analysis released on Tuesday forecast a steady decline in clunker related business even though the Obama administration and Congress added $2 billion to the program in recent days with hopes of matching the success of its first weeks. Sales during that period topped 250,000 and rebates exceeded $1 billion at least, according to government and industry figures.

We see that interest dying down, Senior Analyst Michelle Krebs said in an interview on the consumer auto industry resource group's analysis of buyer intentions. It's still high. It's better than pre-clunker levels, but it's off its peak.

Krebs said the original $1 billion funding for the program was very low in relation to the size of the auto market. This, she said, created a Gold Rush mentality where consumers stormed dealers at the end of July and in the first days of August to cement discounts with rebate funding running low.

The clunker initiative offers rebates of up to $4,500 when consumers trade in older cars for more fuel efficient new ones. Dealers say buyers are trading in mainly sport utilities, pickups and other U.S.-made vehicles for fuel stingy foreign-made passenger cars.

Automakers credited clunker trade-ins for boosting July sales to the best annualized rate for 2009, a year in which carmakers have contended with a devastating decline in business. The horrid, recession-driven sales environment contributed to bankruptcies at General Motors Co and Chrysler this spring.

Both have since emerged from Chapter 11 to an uncertain place in the market with the healthier Ford Motor Co rebounding nicely in July from the brutal sales decline and Japanese powerhouses Toyota Motor Co and Honda Motor Co capitalizing strongly on the clunker fueled consumer shift to passenger cars.

Tammy Darvish of Darcars Automotive Group said showroom traffic has eased for domestic models since the first week of the month, with inventory running low.

Chrysler shut down production during its bankruptcy in April, and GM slowed output significantly for over two months during its restructuring.

Foreign makers, especially Toyota, are still attracting buyers for historic discounts but traffic has eased slightly for those dealers, too, Darvish said.

We don't have as great an inventory as we're used to, but we have enough, Darvish said of hot-selling Toyota Corollas, Camrys and Tacoma pickups.

The Corolla ended July with an average supply of 34 days while the Camry supply averaged 38 days, Toyota spokeswoman Martha Voss said.

Domestic and foreign auto manufacturers remained cautious about boosting production. Memories remain fresh, especially among U.S. manufacturers, of unsold vehicles rushed to market in recent years in response to soaring gasoline prices.

Toyota is increasing production of key models by 65,000 vehicles, which are being shipped to dealers through September, Voss said. Ford's production is running ahead of last year and has said it will disclose plans in September about third quarter production.

GM already plans to increase third-quarter production across its vehicle lineup by 35 percent over the previous three months, officials said. Senior executives said on Tuesday production would go up even more later in the year, with plans to be announced by the end of the month.U.S. Representatives Candice Miller and Fred Upton, both of Michigan where domestic manufacturers are based, are so concerned about shrinking inventories that they asked the Obama administration to intervene.

The inventories of some automakers and dealers have been so depleted that the program's extension may be limited in its effectiveness, they wrote in a letter to Transportation Secretary Ray LaHood.

They asked that clunker rules be modified to allow consumers to reserve a rebate from the manufacturer for a newly ordered car or truck.

This will allow consumers to purchase the vehicle they want even if it is not presently on the dealer's lot, they wrote.

(Reporting by John Crawley; Editing by Richard Chang)