* 2013 current account surplus shrinks to 3.3 trln yen
* Current account in December shows largest deficit on record
* Weak yen pushing up cost of energy imports
* Disappointing exports weighing on growth expectations
TOKYO, Feb 10 (Reuters) - Japan posted its smallest current account surplus on record last year in a worrying sign that sluggish exports and the rising cost of energy imports will hamper economic growth. The deteriorating external position is also bound to put the spotlight back on Japan's ability to service its huge debt, which at over twice the size of its econoy is the worst in the industrialised world. The Ministry of Finance data on Monday also showed the current account balance for December slid to the largest deficit on record as exporters have failed to reap the benefits of a weak currency. Many policy makers expected a falling yen would push up exports and support the economy but lacklustre external demand and declining competitiveness have hampered the trade sector. After stagnating for decades, the government's aggressive fiscal and monetary stimulus policies over the past year have seen the economy rebound. Still, the uneven recovery may prompt officials to consider other options to keep economic growth on track, some analysts say. "Gains in exports are weaker than I expected, reflecting declining competitiveness," said Hiroaki Muto, senior economist at Sumitomo Mitsui Asset Management Co. "The current account can remain in surplus, but the surplus will be small. This is an economic headwind that could place pressure on the government and the Bank of Japan to respond." For 2013, Japan's current account recorded a 3.3 trillion yen surplus, the data showed. This was the smallest surplus in comparable data available from 1985. Last year imports rose 15.4 percent versus a 9.0 percent gain in exports, the data showed. In December, the current account deficit stood at 638.6 billion yen ($6.25 billion), against a median forecast for 707.7 billion yen. The yen has fallen around 23 percent versus the dollar since late 2012 as Prime Minister Shinzo Abe's government embarked on a bold plan to end 15 years of deflation with expanded quantitative easing from the Bank of Japan. Many in the government also expected the yen's fall to boost exports, but this has largely failed to materialise as Japanese companies are producing more goods outside of the country. Japanese companies have also been losing market share to rivals from South Korea and other countries. Years of fiscal stimulus to revive a stagnant economy and surging social welfare costs for a rapidly ageing population have led to Japan running a record 1,000 trillion yen ($10 trillion) in public debt. The deteriorating current account balance has re-focussed attention on the debt pile and on Japan's ability to service it. The increased debt-servicing cost forced Abe to go ahead with a scheduled two-stage sales tax hike from April this year, which is seen as a necessary first step in fixing Japan's tattered finances. The economy is likely to boom until March as consumers rush to beat the sales tax hike, and many analysts agree with the BOJ's view that the pain from the higher tax will be temporary. However, weak exports could mean that the rebound is slower than some economists anticipate.