* Rally puts Brent up for week, U.S. crude nearly flat
* U.S. rig count down for second week in three -Baker Hughes
* Market shifts into backwardation, suggesting tightness (Recasts; updates with settlement prices)
NEW YORK, Aug 18 (Reuters) - Oil prices rose sharply on Friday, as the dollar fell and U.S. drillers cut rigs, feeding a rally that boosted global benchmark Brent crude to a weekly gain while U.S. crude was virtually flat on the week.
U.S. energy firms cut oil rigs for a second week in three, the Baker Hughes energy services firm reported, with drillers cutting spending plans in reaction to declining crude prices.
Drillers cut five oil rigs in the week to Aug. 18, bringing the total count down to 763, Baker Hughes said. <RIG-OL-USA-BHI>
Earlier in the week, government data had suggested that crude output in the United States was still rising.
WTI crude futures for September delivery rose $1.42 to $48.51 a barrel, a 3 percent gain. Brent crude futures for October delivery rose $1.69 to $52.72 a barrel, a 3.3 percent gain.
Brent and U.S. crude prices had both been headed for weekly declines of more than 2 percent, but Friday's sharp rally left Brent with a 1.5 percent weekly gain while U.S. crude finished the week virtually flat, down just 0.3 percent.
Tariq Zahir, founding member at Tyche Capital Advisors, warned that despite Friday's rise, fundamentals for oil remain bearish as U.S. driving season nears an end.
"The main question is whether we will continue to see the kind of inventory draws that may show the supply-demand balance is tightening over the next few weeks," said Gene McGillian, director of market research at Tradition Energy.
Nigeria's crude oil exports are expected to slip to 1.72 million barrels per day (bpd) in October, loading programs showed on Friday.
Signs of supply tightness have started appearing in the United States, the world's biggest oil consumer.
Despite a 13 percent jump in production <C-OUT-T-EIA> since mid-2016 to 9.5 million bpd, the country's commercial crude inventories <C-STK-T-EIA> have fallen 13 percent from their March records to below 2016 levels.
(Additional reporting by Henning Gloystein and Karolin Schaps; Editing by David Evans and David Gregorio)