* Nov gas output 12.6 bcm vs 12.4 bcm in Oct
* Crude oil processing runs at record high in Nov
* Nov crude output rebounds from lowest since at least 2010
* Coal output highest since June
* Data suggests China import demand will remain firm (Adding detail throughout)
BEIJING, Dec 14 (Reuters) - China's coal miners and natural gas producers ramped up output last month at their fastest pace in months to meet surging winter heating demand as utilities and households scrambled for supplies amid a fuel supply crisis, data showed on Thursday.
Producers pumped 12.6 billion cubic meters (bcm) of gas in November, up from 12.4 bcm a month earlier and the highest monthly total since March, according to data from the National Statistics Bureau (NBS).
That likely marks a peak for monthly production with no new projects coming on stream and little room in existing operations to boost supplies further, analysts and experts said.
Major gas fields such as PetroChina's Yanchang and Changqing have been running at full capacity to cope with demand for the fuel for heating since many northern cities reported shortages in November as part of Beijing's drive to cut coal use and curb pollution.
China's coal output last month still hit its highest since June at 299.98 million tonnes, and analysts expect demand in the world's top consumer of the fuel to continue to rise as many homes revert to the commodity for heating due to gas shortages.
Many households are also using electric heaters, drawing on coal-fired power plants.
The data suggests China will need to import more gas and coal to meet extra winter demand, likely adding further support to rallying prices.
Liquefied natural gas (LNG) prices in Asia hit three-year highs earlier this month, while China's thermal coal futures rose to a record 690 yuan per tonne on Thursday.
Domestic LNG prices hit record highs above 8,000 yuan per tonne earlier this month, according to market.yeslng.com, an unregulated online exchange for domestic supplies of the fuel.
NBS spokesman Mao Shengyong told reporters on Thursday that the gas price gains should be a "short-term phenomenon."
For the first 11 months of 2017, China's gas output reached 133.8 bcm, on track to beat the annual record of 136.8 bcm for the whole year of 2016.
China's crude oil processing rate in November rose to 49.43 million tonnes, or 12.03 million barrels per day (bpd), setting a record for a daily basis.
Run rates rose to 11.34 million bpd for the January to November period - higher than the annual record of 10.79 million bpd set last year - and pointing to a 12-month high in store for all of 2017.
Rising diesel and gasoline prices this winter have boosted refining margins and the demand for crude oil.
Domestic crude oil production stood at 15.7 million tonnes, or 3.8 million bpd in November rebounding from 3.77 million bpd last month, the lowest in Reuters records that go back to 2010, as producers continue to tackle dropping output from the country's aging oil wells.
For January-November, China's crude output fell to 175.6 million tonnes, equivalent to 3.8 million bpd.
(Reporting by Meng Meng and Josephine Mason; Editing by Kenneth Maxwell and Tom Hogue)