Brent crude futures were up 9 cents at $61.40 a barrel by 1139 GMT, having gained 2.2pc on Thursday.
US West Texas Intermediate crude futures were down 13 cents at $52.15. WTI also rose 2.2pc in the previous session.
Both contracts were on course to register weekly declines of about 3pc.
The International Energy Agency cut its demand growth forecast for 2019 by 100,000 barrels per day (bpd) to 1.2 million bpd, citing worsening prospects for world trade.
However, the Paris-based agency said it expects demand growth to climb to 1.4 million bpd for 2020.
On Thursday the Organization of the Petroleum Exporting Countries cut its 2019 forecast for growth in global oil demand even lower than the IEA, to 1.14 million bpd.
The attacks on oil tankers near Iran and the Strait of Hormuz pushed up oil prices by as much as 4.5pc on Thursday.
It was the second time in a month tankers have been attacked in the world's most important zone for oil supplies as tensions increase between the United States and Iran.
Washington blamed Iran for Thursday's attacks, prompting a denial and criticism from Tehran.
"Yesterday's attacks on the Japanese and Norwegian tankers in the Gulf of Oman underscore the severity of the security risks stemming from the Iran crisis and the difficulty of achieving a diplomatic off-ramp as long as the crippling US sanctions remain in place," RBC bank said.
Tensions in the Middle East have escalated since US President Donald Trump withdrew from a 2015 multinational nuclear pact with Iran and reimposed sanctions, especially targeting Tehran's oil exports.
Iran, which has distanced itself from the previous attacks, has said it will not be cowed by what it describes as psychological warfare.
US Secretary of State Mike Pompeo said the United States has assessed that Iran was behind the attacks on Thursday.
The US military later released a video that it said showed Iran's Revolutionary Guard removing an unexploded mine from the side of a Japanese-owned oil tanker.
In a statement on Thursday evening, the Iranian mission to the United Nations said Tehran "categorically rejects the US unfounded claim with regard to 13 June oil tanker incidents and condemns it in the strongest possible terms".