Brent crude, the international oil price benchmark, rose above $51 a barrel at one point during afternoon trading in New York, before paring gains to close a little below that threshold. It was holding at around $50.80 a barrel in London this morning.
Its US counterpart, West Texas Intermediate, was three per cent higher at more than $48 a barrel and remained above that level in early trading in London.
The latest jumps added two to three per cent to the benchmarks compared to Wednesday and left them both around 22 per cent above the low reached earlier this month, says Market Watch.
Both Brent and WTI are now officially in a "bull market" run, sitting near two-month highs immediately on the back of a fall into a "bear market" last month.
Ongoing speculation that the world's largest producers, including the Saudi Arabia-led Opec cartel and Russia, could agree a deal to freeze production next month has helped boost prices.
A deal would encourage investors to believe that a two-year supply glut is coming to an end - something US reserves data this week might also have suggested with a surprise fall in both raw crude and petrol stocks.
However, some analysts remain unconvinced. A previous proposal to cap production collapsed in April and Opec member Iran has hinted it may again hold out as it returns from international sanctions.
"Some believe - or more appropriately, hope - that [Opec] may come up with a plan to support prices at its informal meeting next month, something which we doubt will happen," Fawad Razaqzada, a market analyst at Forex, told Reuters