* Push for gas goes too far, too soon -CNPC researcher
Millions of homes, factories already converted
* Beijing under increasing pressure to clear skies (Updating throughout)
BEIJING, Dec 7 (Reuters) - Beijing has eased a push to convert northern cities to gas or electric heating this winter, after two provinces warned of gas shortages and reports of freezing classrooms deepened concerns about a winter heating crisis, local media said on Thursday.
The deceleration is the first admission from the central government that its effort to switch households and factories in the country's smoggiest cities away from coal may have been implemented too quickly, and without the critical infrastructure and domestic output to meet the resulting surge in demand.
China's Ministry of Environment has told northern regions that have not converted to gas or electric heating may burn coal or other fuels instead, financial magazine Caixin reported.
Caixin cited regulatory sources who confirmed to the publication that official orders were issued in a document.
"It is not wrong for Beijing to push the coal-to-gas switch, but the process was a bit too fast and outpaced the market's capacity," said Xu Bo, a researcher with CNPC's Research Institute of Economics and Technology.
Suspending the project that stretches across 28 northern cities may have a limited impact as more than 4 million homes have already installed gas-fired radiators, while tens of thousands of factories have ripped out coal-fueled boilers.
The extra consumption since the winter heating season started in mid-November has already triggered a surge in domestic gas prices to record highs and forced companies to take unprecedented, costly steps to ensure supplies.
Chinese LNG prices have surged over the past month, hitting record highs last week above 8,000 yuan ($1,210) per tonne, according to market.yeslng.com, an unregulated online exchange for domestic supplies of the fuel.
The retreat is a blow to the government's years-long push to wean China from coal, its favorite fuel, to help clear the nation's smoggy skies, which have become a hot-button issue.
Beijing is under increasing social and economic pressure to deal with the chronic hazardous air that blankets the north and threatens people's health.
For now, though, concerns about keeping the world's most populous nation warm have taken precedence.
On Thursday, the official English language newspaper China Daily said the Ministry of Education demanded "immediate" action to ensure classrooms are warm enough after local media reported students were showing symptoms of frostbite due to delays in heating supplies in Hebei province.
Heating to some rural schools in Hebei's Quyang county has been delayed, forcing classes outside into the sun's warmth, the China Youth Daily reported.
Cities that have already switched to gas should ensure steady supplies and stable prices of gas and electricity, the environment ministry said in its document, according to Caixin.
Still, state oil and gas producer China National Petroleum Corp (CNPC) joined a chorus of warnings across the industry on Thursday warning of shortages if the winter is extremely cold.
Wood Mackenzie estimates heating needs alone will add 10 billion cubic meters (bcm) to China's gas demand, the equivalent of Vietnam's annual consumption. China is expected to use a record of about 230 bcm this year.
"It will take time to improve the infrastructure, so I think the gas shortage problem in China will remain in future years, but should not be as bad if we learn from the lesson," said CNPC researcher Xu.
($1 = 6.6143 Chinese yuan)
(Reporting by Josephine Mason, Muyu Xu and Beijing news monitoring desk; Editing by Richard Pullin and Tom Hogue)