Toyota Motor Corp told its United States dealers last week that the company had 45 days of inventory and was working hard to get the word out that it was "open for business."

In a letter obtained by Reuters, US Toyota brand sales chief Bob Carter told dealers the company was in a "healthy position" as it moved toward a full production schedule.

The company recently announced that eight of its North American-built models, including the Camry and Corolla, would return to 100 percent production in June.

"This is well ahead of our previously announced timeline of November/December," Carter said in the letter.

The earthquake that rocked northeastern Japan on March 11 forced Toyota and other Japanese auto makers to cut output at home and abroad as they struggled to secure vital auto parts. The subsequent nuclear disaster and power shortages further complicated problems.

But Toyota has moved to restore production more quickly than many analysts expected. In the letter, Carter reiterated the auto maker's US output would be 70 percent of normal volume in June, up from 30 percent in May.

Toyota forecast a full return to production for all models and factory lines by November or December.

At 45 days, Toyota's current inventory levels is just five days less than its May 2010 inventory level of 50 days.

But Toyota's sales rate has dropped even more quickly than its inventory level, Edmunds.com Chief Executive Jeremy Anwyl said. He said data show that Toyota's supply of vehicles is outpacing current demand.

Analysts said Toyota's sales have been pinched because curbed auto production has raised car prices amid rising fuel prices.