WASHINGTON (Reuters) - U.S. President Barack Obama dismissed Mitt Romney's comments this week claiming credit for the recovery of the U.S. auto industry, saying his Republican rival's plan would have sunk General Motors Co and Chrysler Group LLC.

There was no private sector option to save the car makers in 2009 and Romney's stance would have cost many jobs, the Democratic president, who is seeking a second term in office, told ABC News in an interview that aired on Thursday.

"I think this is one of his Etch-a-Sketch moments. I don't think anybody takes that seriously," Obama said, referring to a common U.S. drawing toy that resets when shaken that gained renewed prominence when cited by a Romney aide earlier this year.

"People remember his position, which was, "Let's let Detroit go bankrupt," and his opposition to government involvement in making sure that GM and Chrysler didn't go under," he said in the interview taped on Wednesday.

"Had we followed his advice, at that time, GM and Chrysler would have gone under. And we would have lost probably a million jobs throughout the Midwest."

Romney, the presumptive Republican presidential candidate, opposed Obama's 2009 bailout of General Motors and Chrysler. His father, who had run an auto company, was a popular governor of Michigan, homebase to the city of Detroit and the U.S. automotive industry.

On Monday, Romney - a former business executive and one-time governor of Massachusetts - told an ABC affiliate that he had "pushed the idea of a managed bankruptcy, and finally when that was done and help was given, the companies got back on their feet."

"So I'll take a lot of credit for the fact that this industry's come back," Romney said hours before making a speech at a local university in Michigan, according to ABC News.

Obama said the issue highlighted the differences between him and his challenger in the November 6 election.

"There is gonna be a fundamental difference. I think the auto example is just one of many differences that we're gonna have on the economy," Obama said.

In 2009, Obama led a controversial $80 billion bailout of the automakers. A year earlier, Romney penned an opinion piece calling for the companies to go bankrupt that has dogged him on the campaign trail, particularly in Michigan.

Chrysler Group LLC is now majority-owned and managed by Italy's Fiat SpA. Both GM and Chrysler have moved from the government-funded bankruptcies to renewed profits.

(Reporting By Susan Heavey; editing by Mohammad Zargham)