Oil prices rose on Tuesday, lifted by indications that supply is gradually tightening, especially in the United States.

Brent crude futures, LCOc1 the international benchmark for oil prices, were at $51.91 per barrel at 0607 GMT, up 25 cents, or 0.5 percent, from their last close.

U.S. West Texas Intermediate (WTI) crude futures CLc1 were at $47.60 a barrel, up 23 cents, or 0.5 percent.

"U.S. crude oil stocks have been falling consistently in recent weeks. If the downtrend in oil inventories is maintained, then a bullish case can be made for oil, especially given the ongoing supply restrictions from OPEC and Russia," said Fawad Razaqzada, market analyst at futures brokerage Forex.com.

U.S. commercial crude inventories have fallen by almost 13 percent from their March peaks, to 466.5 million barrels. C-STK-T-EIA

And although U.S. crude production has broken through 9.5 million barrels per day (bpd), its highest since July 2015, analysts said growth may soon slow as U.S. energy firms are cutting the amount of rigs drilling for new oil. C-OUT-T-EIA RIG-OL-USA-BHI

Erik Norland of CME Group, a major commodity exchange, said "it looks like the growth in U.S. production is quickly running out of steam and, all else being equal, this should be good news for OPEC and the price of oil".

The Organization of the Petroleum Exporting Countries (OPEC) together with non-OPEC producers including Russia has pledged to hold back around 1.8 million bpd of output between January this year and March 2018 in order to tighten supplies and prop up prices.