* Russia clarifies Putin recognizes possibility of deal extension
* Brent's bull run was longest in 16 months
* U.S. crude set for biggest weekly loss in three months
* Several U.S. Gulf oil facilities shut ahead of storm Nate (Adds Russia news, updates prices)
AMSTERDAM, Oct 6 (Reuters) - Oil prices fell on Friday at the end of a week that saw profit-taking and the return of oversupply concerns lead the market lower, snapping a multi-week bull run that was Brent's longest in 16 months.
Benchmark Brent crude futures were down 26 cents at $56.74 a barrel at 1112 GMT, set for a 1.5 percent loss on the week and snapping a five-week winning streak that was the longest since June 2016.
U.S. West Texas Intermediate (WTI) crude was at $50.27, down 52 cents. It was set to close the week down nearly 3 percent, the biggest weekly loss in three months.
Russia on Friday clarified remarks on the oil market made by President Vladimir Putin 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, incentivised by a hefty WTI discount to Brent prices.
"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.
"I expect Brent to drop below $55 a barrel and WTI below $50 in the next couple of days."
U.S. government data showed this week that crude exports had risen to a record of nearly 2 million barrels per day.
Investors were also wary of tropical storm Nate shutting down some oil production in the Gulf of Mexico ahead of its expected arrival in the area as a hurricane on Sunday.
"The biggest impact (from Nate) could be on gasoline prices, depending on how many refineries are forced to shut down. But I don't think we will see another bull run," Schallenberger said.
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 reporting by Henning Gloystein in Singapore; Editing by Dale Hudson and Jason Neely)