Brent crude futures LCOc1 were up 63 cents at $50.27 a barrel at 0941 GMT (05:41 a.m. EDT). U.S. crude futures CLc1 were up 60 cents at $49.22 a barrel.
Traders said oil prices rose on a sharp fall in the dollar .DXY on Friday after weak U.S. jobs data sparked concerns over the state of the world's biggest economy, cutting expectations of a near-term cut in U.S. interest rates.
A weaker dollar supports fuel demand in the rest of the world as it makes dollar-traded oil imports cheaper.
Traders will be watching Fed Chair Janet Yellen's speech at 1630 GMT (12:30 p.m EDT) on Monday for hints of a potential rate move.
"Futures have been trading in a small range for the last 10 days. If we want to see any more upward movement then we need to see strength from products...but so far the gasoline crack has been capped," said Olivier Jakob, oil analyst at Petromatrix in Switzerland.
The Muslim holy month of Ramadan starts on Monday and is seen as supportive of prices as driving demand picks up in most Muslim-dominated countries.
Traders said prices were also propped up by attacks on oil infrastructure in Nigeria, which has already sent the country's output to more than 20-year lows.
So far, supply cuts like those in Nigeria or Libya, have been met by rising output in the Middle East, especially Iran, which has ramped up output since the end of international sanctions against it in January.
But Iran is returning to international oil markets more quickly than expected and is quickly returning to its maximum capacity.
This means that further disruptions in global supplies might not be compensated by rising Iranian output.
Oil's price rally, however, was capped on signs of increased output in the United States where energy firms this week added rigs drilling for oil for the second time this year, energy services company Baker Hughes Inc (BHI.N) said on Friday.
Rising prices have encouraged producers to cautiously increase activity. Drillers added nine oil rigs in the week to June 3, raising the rig count to 325 but still well below the 642 at work a year earlier, Baker Hughes said.
"While not enough to materially change the outlook for U.S. production ... there are some early signs that rigs may be returning in the best acreage, namely the Permian Basin," Morgan Stanley said.
U.S. crude oil production has fallen by 5.4 percent since January and by almost 10 percent since mid-2015 to 8.74 million barrels per day.