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TOKYO (Reuters) - Japanese exports rose 15.3 percent in December but imports outpaced shipments due to a weak yen and subsequent higher fuel import costs, resulting in a record trade deficit for 2013, Ministry of Finance data showed on Monday. The rise in exports compared with the median estimate of a 17.8 percent increase in a Reuters poll of economists and followed an 18.4 percent gain in November. It marks a 10th straight month of gains helped by a weak yen and car shipments. Imports rose 24.7 percent year-on-year in December, compared with an expected rise of 26.1 percent, due to the weak currency and a rise in demand for fossil fuels to make up for nuclear energy lost since the 2011 Fukushima disaster. As a result, the country's trade balance stood at a deficit of 1.3 trillion yen ($12.7 billion) in December, against a 1.2225 trillion yen deficit expected by analysts, posting a record 18 straight months of deficits. For 2013, Japan logged a record annual trade gap of 11.47 trillion yen, widening from 6.94 trillion yen in the previous year and marking a third straight year of deficit, the longest run on record, dating back to 1979. ($1 = 102.3550 Japanese yen) (Reporting by Tetsushi Kajimoto; Editing by Chang-Ran Kim and Dominic Lau)