* Oil output in 2013 up almost 1.4 pct at 10.51 mln bpd
* Budget tested by high social spending, Olympics
* China set to become largest customer
By Vladimir Soldatkin
MOSCOW, Jan 2 (Reuters) - Russia retained the title of the world's top oil producer with 2013 output reaching a post-Soviet high as rising exports to China and strong prices allow the Kremlin to maintain record spending from an overstretched budget.
Energy has been the engine of Russia's growth during more than a decade of leadership by President Vladimir Putin, with oil and gas accounting for more than half of budget revenues.
But the government, which has amassed some of the world's largest foreign exchange reserves of over $500 billion, has been increasingly overstretching its finances due to social spending promised by Putin before the 2012 election as well as a swelling $50 billion budget for the 2014 Winter Olympics.
Keeping oil output high has therefore been a priority for the government. The rise has defied predictions that new fields in East Siberia and the Arctic will be unable to compensate for declines from ageing oilfields in West Siberia.
"Enough investment is being made to slow declines in West Siberia and increase production in East Siberia in order to make for small net production increases," analysts from the International Energy Agency (IEA) told Reuters on Thursday.
The IEA, the West's energy watchdog, expects Russian production to remain flat at around 10.5 million barrels per day (bpd) until the end of the decade, and then decrease to about 9.5 million bpd by 2035.
The IEA says that key to maintaining Russian production levels would be the Kremlin's ability to extract hard-to-recover oil, emulating U.S. successes, and to encourage more production in remote Arctic and East Siberia regions.
Despite record output, Russia's budget funding gap could reach some $300 billion between 2017 and 2020 should spending remain high and oil prices drop, according to the Finance Ministry's budget strategy to 2030.
That is three times the current value of the Reserve Fund, a rainy-day collection of windfall energy revenues.
Last year's budget was estimated to balance at an oil price of $110 per barrel and this year's at some $115 a barrel, Alfa Bank chief economist Natalia Orlova said.
That is dangerously close to or even higher than current prices for benchmark Brent crude, which stood at an average of below $110 in 2013 and are expected to remain under downward pressure in years to come due to a U.S. shale oil boom and a possible rise in exports from Iran.
Russian energy ministry data showed on Thursday that the country's oil output rose to a post-Soviet high of 10.51 million bpd in 2013, up almost 1.4 percent from 2012.
December's monthly production averaged 10.63 million bpd, also a post-Soviet high.
Russian output likely stayed above that of Saudi Arabia, which kept production steady at around 9.7 million bpd in October and November. Saudi data for December is not yet available.
Almost all large Russian oil firms increased output in 2013 as they boosted drilling, including Lukoil, Russia's second-largest oil producer and top non-state oil company, which had logged declines in the previous three years.
State-controlled Rosneft, the world's top listed oil producer, posted a dramatic jump in output to 3.1 million bpd thanks to the acquisition of rival TNK-BP and production increases in East Siberia.
The year was also marked by a further diversion of Russian oil to China, away from saturated European markets, as eastbound flows rose by almost a fifth to 740,000 bpd.
As Russia agreed to increase deliveries further to China in coming years, the Asian giant will likely replace Germany as the largest customer for Russian pipeline oil in the first quarter of 2014.
Despite the jump in eastbound flows, Russian oil exports outside the former Soviet Union fell by around 2.5 percent to 4.53 million bpd as Russia ramped up oil refining.
Domestic refining rose by 180,000 bpd, reflecting the country's $55 billion programme launched in 2011 to modernise its refineries and encourage exports of high-quality oil products.
Gazprom, the world's top gas producer, saw its output slip to 1.30 billion cubic metres (bcm) per day from 1.31 bcm per day in 2012 although its exports to Europe jumped 16 percent to a record 161.5 billion cubic metres.