* Russia clarifies Putin recognizes possibility of deal extension
* Several U.S. Gulf oil facilities shut ahead of storm Nate
* U.S. oil drillers cut rigs for 4th week in five -Baker Hughes (Updates prices, adds Baker Hughes rig count report)
NEW YORK, Oct 6 (Reuters) - Oil futures plunged over 2 percent on Friday, and were set to end Brent's longest multi-week rally in 16 months following profit taking and the return of oversupply concerns.
Benchmark Brent crude futures were down $1.26 at $55.74 a barrel by 2:01 p.m. EDT (1801 GMT), set to snap a five-week winning streak that was the longest since June 2016.
U.S. West Texas Intermediate (WTI) crude was at$49.35, down $1.44 or 2.8 percent on the day.
"Yesterday we had Russia and the Saudis talking about extending cooperation, and today we saw a little bit of backtracking with respect to additional cuts in production." said Houston-based consultant Andrew Lipow. "What the market gained yesterday is clearly being given back today."
Russia on Friday clarified remarks made by President Vladimir Putin about the oil market earlier this week, saying he did not propose extending a global oil output cut deal but said he recognized it was a possibility.
The prospect of extended oil production cuts by the Organization of the Petroleum Exporting Countries and other producers led by Russia had supported prices in recent sessions.
Saudi Arabia's energy minister said on Thursday he was "flexible" about prolonging the production-curbing pact until the end of 2018.
However, concerns linger about growing U.S. crude exports, due to a hefty WTI discount to Brent prices, which makes U.S. oil more competitive.
"We have a couple of bearish factors like a new record for U.S. crude exports, the reopening of Libya's biggest oilfield, a new year high in U.S. crude production and the recent strength of the U.S. dollar," said Frank Schallenberger, head of commodity research at LBBW in Stuttgart.
A stronger dollar, which makes greenback-denominated more expensive for buyers in other currencies, also led to further losses in the oil market on Friday. The dollar hit a 10-week high after data showing the largest gain in U.S. wages since December 2016 bolstered bets on an interest rate hike by year-end.
U.S. government data showed this week that crude exports had risen to a record of nearly 2 million barrels per day as domestic production grows.
The Baker Hughes' report on the U.S. oil drilling rigs, an early indicator of future output, showed the rig count fall in for the fourth week out of the last five.
Investors were also watching Tropical Storm Nate as companies shut down some oil production in the Gulf of Mexico ahead of its expected arrival in the area as a hurricane on Sunday.
In the Gulf of Mexico, BP and Chevron were shutting production at all platforms, while Royal Dutch Shell and Anadarko Petroleum suspended some activity. Exxon Mobil, Statoil and other producers have withdrawn personnel.
Additional production cuts are expected as the forecast track cuts through the heart of Gulf oil production, Lipow said. (Additional reporting by Henning Gloystein in Singapore and Karolin Schaps in Amsterdam; Editing by Marguerita Choy and Susan Fenton)