NEW YORK, Aug 29 (Reuters) - U.S. auto insurance customers are most satisfied with one of the nation's oldest mutual car insurance companies and least happy with the world's largest insurer, according to an annual survey released on Tuesday by J.D. Power and Associates.

J.D. Power, a market research firm specializing in customer satisfaction surveys, found that clients' favorite company dealing with the general public was Amica Mutual Insurance Co. of Lincoln, Rhode Island. It was the seventh consecutive time that Amica -- which was founded in 1907 and claims to be the the nation's oldest mutual car insurer -- had taken the top spot, Power said.

USAA, a military insurer, actually came in higher than Amica but is not open to the general public, Power said.

The lowest score went to New York-based American International Group Inc. (AIG.N: Quote, Profile, Research), the world's biggest insurer by market value.

Amica could not be reached for comment on the survey. Chris Winans, a spokesman for AIG, said the flagship of its auto insurance operations, AIG Direct, had done well in other Power surveys. But the company was also obligated by state regulators to take on many clients who had a higher risk of accidents, Winans said. AIG's auto business is a small part of the total company.

With the exception of Geico, a unit of Berkshire Hathaway Inc. (BRKa.N: Quote, Profile, Research), most of the major publicly traded auto insurers came in below the average.

They included -- in descending order -- Allstate Corp. (ALL.N: Quote, Profile, Research), Hartford Financial Services Group Inc. (HIG.N: Quote, Profile, Research), MetLife Inc. (MET.N: Quote, Profile, Research), St. Paul Travelers Cos. Inc. (STA.N: Quote, Profile, Research) and Progressive Corp. (PGR.N: Quote, Profile, Research).

Power said the key factor in satisfaction was only having to contact the insurer once to resolve an issue. The more contacts, the less satisfaction. The same was true when waiting for an issue to be resolved.

"For customers who file a ... claim with their auto insurer, time is critical," said the Power report.

The one time clients wanted to talk to their carriers, said the Power report, was for an annual review of their insurance needs. Currently only half of auto insurance customers report having been offered such a review.

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