WASHINGTON, Oct 15 (Reuters) - U.S. import prices rebounded in September, lifted by higher food and energy costs, but underlying imported inflation showed signs of moderating. Import prices rose 0.4% last month after falling 0.3% in August, the Labor Department said on Friday. In the 12 months through September, prices shot up 9.2% after advancing 8.9% in August. Economists polled by Reuters had forecast import prices, which exclude tariffs, increasing 0.6%. The government reported this week that strong food prices and rents pushed up consumer inflation in September, while higher energy costs kept producer prices elevated. The price of Brent crude has shot above $80 a barrel. Imported fuel prices increased 3.7% last month after declining 3.0% in August. Petroleum prices rebounded 3.9%, while the cost of imported food accelerated 1.3%. Excluding fuel and food, import prices dipped 0.1%. These so-called core import prices fell 0.1% in August and were up 4.7% on a year-on-year basis in September. The report also showed export prices nudged up 0.1% in September after rising 0.4% in August. Prices for agricultural exports fell 1.7%. Nonagricultural export prices gained 0.3%. Export prices rose 16.3% year-on-year in September after increasing 16.8% in August.