Brent crude futures gained $1.12, or 1.8%, to $62.79 a barrel, by 1:17 p.m. EDT (1717 GMT).
They have agreed to cut their combined production by 1.2 million barrels per day, or more than 1% of global output, from January 1 until the end of June in order to support oil prices and balance the global crude market.
Brent posted its third weekly decline, dropping almost 2%, while WTI gained about 1% for the week.
Saudi Energy Minister Khalid al-Falih said OPEC is close to agreeing to extend an oil supply-cutting agreement beyond June.
A deal by the Organization of the Petroleum Exporting Countries (OPEC) and other producers, including Russian Federation, to reduce output by 1.2 million barrels per day (bpd) runs out at the end of this month.
Supply has also been limited by USA sanctions on oil exports from Venezuela and Iran. On Thursday, Washington tightened pressure on Venezuela's state-owned oil company by making clear that exports of diluents by global shippers could be subject to sanctions.
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That put both contracts in bear territory, having lost more than 20% from peaks reached in late April.
The number of USA oil rigs dropped 11 to 789 for the week ending June 7, United States energy services firm Baker Hughes reported on Friday.
However, its gains remain limited since uncertainty continues over the trade war causing a possible slowdown in global economy.
The Trump administration made a decision to impose a 5% tariff on Mexican goods that come into the US and said the rate would go up gradually if Mexico does not make efforts to halt illegal migration of people into the U.S.
"There's talk now that the US might not put on the Mexico tariffs, and that's pushed equities up, and you've got a little bit of short covering based on that statement", said Dominick Chirichella, director of risk management and advisory services at EMI DTN in NY. Although the Trump administration is said to be moving forward to implement the proposed tariff from Monday, some analysts and participants believe Trump will delay imposing the tariffs for now. "In response, we have revised our third-quarter forecast for Brent down to $66 (previously $73)", Commerzbank said in a note.
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