(Adds NYMEX gasoline closing price, fuel costs in cities) By Tom Doggett WASHINGTON, May 29 (Reuters) - The average U.S. retail price for gasoline dipped nearly a penny in the latest week, after surging to record highs for two weeks in a row, the government said on Tuesday. The national price for regular unleaded gasoline dropped 0.9 cent over the last week to $3.21 a gallon, still up 34 cents from a year ago, according to the federal Energy Information Administration's nationwide survey of service stations. The latest pump price is off the all-time high fuel cost of $3.29 a gallon, when adjusted for inflation in 2007 dollars, reached in March 1981 during the war between Iran and Iraq, the EIA said. The agency had not expected gasoline prices to start falling until sometime in June. The dip follows a rise in U.S. gasoline inventories, as more oil refineries come back online to make motor fuel while gasoline imports also remain strong. Worries about gasoline supplies eased in Tuesday trading at the New York Mercantile Exchange, where gasoline for June delivery fell almost 10.6 cents, or 4.4 percent, to settle at close to $2.30 a gallon. In the EIA's new weekly survey, gasoline was the most expensive on the West Coast, down 2.3 cents to $3.35. Among major cities, Chicago had the highest pump costs at $3.62 a gallon, up 8.9 cents. The Gulf Coast states had the lowest regional price at $3.07 a gallon, down 2.5 cents. Houston had the cheapest pump price at $3 a gallon, up 1.9 cents. The EIA also reported gasoline prices were down 4.2 cents at $3.38 in Los Angeles, down 5.5 cents at $3.36 in Seattle, up 13.4 cents at $3.34 in Cleveland, down 0.1 cent to $3.30 in Denver, up 2.7 cents at $3.20 in Miami and up 3.2 cents at $3.14 in New York City. The EIA has warned that gasoline prices could rise again this summer, especially if a major hurricane hits the Gulf Coast and disrupts petroleum supplies like storms Katrina and Rita did in late 2005. Government officials and oil industry representatives will discuss on Wednesday the preparations they've taken to keep oil supplies flowing during the upcoming hurricane season.