* Several U.S. Gulf oil facilities shut down ahead of storm Nate
* But markets remain supported by prospect of extended output cuts
SINGAPORE, Oct 6 (Reuters) - Oil markets opened cautiously in Asia on Friday as traders monitored a tropical storm heading for the Gulf of Mexico and as China remained closed for a week-long public holiday.
But the prospect of extended oil production cuts led by the Organization of the Petroleum Exporting Countries (OPEC) helped support prices.
U.S. West Texas Intermediate (WTI) crude futures were trading at $50.73 per barrel at 0016 GMT, down 6 cents from their last close.
Brent crude futures, the international benchmark for oil prices, were down 6 cents at $56.94 a barrel.
Oil market activity was subdued on Friday, due to the ongoing Golden Week holiday in China and because traders were monitoring tropical storm Nate, which is threatening to disrupt the oil industry in the Gulf of Mexico just weeks after several hurricanes pummeled the region, knocking out many oil producing and processing facilities.
The Louisiana Offshore Oil Port (LOOP), one of the country's most important fuel handling facilities in the Gulf of Mexico, said early on Friday that it had suspended operations until the weather improves.
Nate is currently off the coast of Nicaragua and heading northwest into a region of the Gulf of Mexico populated by offshore oil platforms which pump more than 1.6 million barrels of crude per day (bpd), about 17 percent of U.S. output, according to government data.
BP and Chevron were shutting production at all Gulf platforms, while Royal Dutch Shell and Anadarko Petroleum suspended some production and drilling activity in the Gulf. Exxon Mobil, Statoil and other producers have withdrawn personnel from their platforms.
Despite this, markets were not far off their closing levels from the previous day, when prices rose by around 2 percent on the prospect of an extended production cut deal lead by OPEC and Russia.
King Salman of Saudi Arabia, OPEC's de-facto leaders, met with Russian President Vladimir Putin in Moscow on Thursday to discuss, among other things, oil policy.
Saudi Arabia made no firm pledge to extend a deal between OPEC, Russia and other producers on cutting supplies but said it was "flexible" regarding Moscow's suggestion to prolong the pact until the end of 2018.
"The visit raised the possibility of the current production cut agreement being extended if the crude oil inventories remain stubbornly high," ANZ bank said.
A deal to cut around 1.8 million bpd in production has been in place since January and is currently due to expire at the end of March 2018.
(Reporting by Henning Gloystein; Editing by Joseph Radford)