Benchmark crude prices were still on track for their biggest weekly decline in seven weeks, however, having fallen sharply earlier in the week on concerns over global oil demand amid slowing economic growth.
Brent crude futures were up $1.11, or 1.78%, at $63.04 a barrel by 1037 GMT, having risen as high as $63.32. Brent fell 2.7% on Thursday, its fourth straight session of losses, and was set for a weekly drop of around 5%.
West Texas Intermediate (WTI) crude futures were $0.81, or 1.44%, higher at $56.11 per barrel after touching $56.36. They ended 2.6% lower in the previous session and were headed for a weekly decline of around 6%.
Indications that the US Federal Reserve will cut rates aggressively to support the economy were also behind Friday's gains, said Stephen Innes, Managing Partner at Vanguard Markets.
"The Fed backstop and the report of the US Navy shooting down an Iranian drone are providing a modicum of support for oil markets amidst a very bearish landscape," he said.
The United States said on Thursday that a US Navy ship had "destroyed" an Iranian drone in the Strait of Hormuz after the aircraft threatened the vessel, but Iran said it had no information about losing a drone.
Also on Thursday, two influential Federal Reserve officials sharpened the public case for acting to support the US economy, reviving bets the central bank may deliver a larger-than-expected cut this month.
Still, the longer-term outlook for oil has grown increasingly bearish.
The International Energy Agency (IEA) is reducing its 2019 oil demand growth forecast to 1.1 million barrels per day (bpd) from 1.2 million bpd previously due to a slowing global economy amid a US-China trade spat, its executive director said on Thursday.
The IEA may cut further if the global economy and especially China shows further weakness, Fatih Birol told Reuters.
"Macroeconomic concerns, uncertainty on trade discussions and increasing oil supply from the US continued to weigh on sentiments," said Warren Patterson, head of commodities at ING.
Bank of America Merrill Lynch said any start of US-Iran talks or a US-China trade deal would reduce volatility and anchor Brent oil prices in a $60-67 per barrel range.
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