Brent futures for May settled $1.64 higher, or 2%, at $83.55 a barrel. The April Brent futures contract expired on Feb. 29 at $83.62 a barrel.
U.S. West Texas Intermediate (WTI) for April rose $1.71, or 2.19%, to $79.97 a barrel.
For the week, Brent added around 2.4% following the switch in contract months, while WTI gained more than 4.5%.
"The expectation that OPEC+ is going to continue with their voluntary production cuts well into the second quarter of 2024 is the main focus on the market," said Andrew Lipow, president of Lipow Oil Associates.
A decision on extending OPEC+ cuts is expected in the first week of March, sources have said, with individual countries expected to announce their decisions.
"Sticking to the voluntary production cuts until the end of the year would be a strong signal and should therefore be seen as price-positive," Commerzbank analyst Carsten Fritsch said.
A Reuters survey showed the Organization of the Petroleum Exporting Countries pumped 26.42 million barrels per day (bpd) in February, up 90,000 bpd from January.
Strong expectations of Saudi Arabia keeping term prices of crude it sells to Asian customers little changed in April from March levels also underpinned the market on Friday.
The oil rig count, an early indication of future output, rose by three to 506 this week, the highest since September.
On the demand side, Chinese manufacturing activity shrank for the fifth straight month in February, an official survey showed.
Euro zone inflation fell in February according to Eurostat, but both the headline figure and core inflation, which strips out volatile food and fuel prices, just missed analysts' expectations.
Supporting prices, the U.S. personal consumption expenditures (PCE) index showed January inflation in line with economists' expectations on Thursday, reinforcing market bets for a June interest rate cut.
Money managers raised their net long U.S. crude futures and options positions in the week to Feb. 27, the U.S. Commodity Futures Trading Commission (CFTC) said.
