The international oil benchmark rose as high as $65.10, pushing past $65 for the first time this year. It slipped back to $64.68 by 1045 GMT, up 11 cents.
That equated to a 0.2 percent gain, keeping Brent near three-month highs and set for a more than 4 percent gain on the week.
US West Texas Intermediate crude futures were at $54.49 a barrel, up 8 cents from their last settlement.
The Organization of the Petroleum Exporting Countries (OPEC) and allies led by Russia started voluntary production cuts last month, aiming to tighten the market.
Top exporter and de facto OPEC leader Saudi Arabia said on Tuesday it would cut more than half a million barrels per day (bpd) more in March than the deal called for, sending prices surging.
Prices were also buoyed by the partial closure of Saudi Arabia's Safaniya, its largest offshore oilfield with production capacity of more than 1 million bpd.
The shutdown occurred about two weeks ago, a source said, and it was not immediately clear when the field would return to full capacity.
"Brent should average $70 per barrel in 2019, helped by voluntary (Saudi, Kuwait, UAE) and involuntary (Venezuela, Iran) declines in OPEC supply," Bank of America Merrill Lynch said in a note.
The bank said it expects a drop of 2.5 million bpd in OPEC supply in the fourth quarter of 2019, from a year earlier.
However, the global supply picture remains uncertain.
US oil production is on the rise, while the seizure of Libya's main oilfield by Eastern armed forces this week could lead to its reopening.
But US sanctions on Venezuela and Iran have have helped to tighten global supply and security threats could threaten Nigerian production after general elections this weekend.
"Looking ahead, the prognosis for Venezuela and Iran remains skewed to the downside. As such, they should continue to act as important pillars of price support. The same, however, can't be said for Libya," said Stephen Brennock of oil broker PVM.
"This risks throwing a spanner in the works for OPEC's rebalancing ambitions and, therefore, the price recovery."
Faltering global economic growth is also a concern, with signs of a slowdown now abundant in Europe, Asia and the United States, which could lead to slowing growth in fuel demand.