TOKYO, Jan 24 (Reuters) - Japanese exports fell 5.8 percent in December from a year earlier, bringing the country into a record trade deficit for 2012, Ministry of Finance data showed on Thursday, suggesting it will take more time for exports to stabilise after a slowdown in overseas economies. The fall in exports, which are a key driver of the world's third-largest economy, compared with the median forecast for a 4.2 percent decline in a Reuters poll of economists. It was the seventh straight month of declines, and followed a 4.1 percent year-on-year fall in November. Exports to China, the top destination for Japanese shipments, dropped 15.8 percent in the year to December and those to Europe declined 11.1 percent. Imports rose 1.9 percent from a year earlier. The trade balance came to a deficit of 641.5 billion yen ($7.25 billion) in December, versus a 534.0 billion yen deficit projected by economists. It was the sixth straight month of deficits.