Modest improvements in the European economy balanced against sentiments on market trajectory from the IEA, giving oil prices a slight lift early Thursday.

Crude oil prices have been on a general rally amid anticipation that Russia and some members of the Organization of Petroleum Exporting Countries will agree at meetings this weekend in Doha to hold production steady at January levels in an effort to stabilize the market.

In its monthly report, the International Energy Agency attributed the recent increase in oil prices largely to expectations about the Doha meetings.

"We cannot know the outcome but if there is to be a production freeze, rather than a cut, the impact on physical oil supplies will be limited," the report read.

Crude oil prices were nevertheless moving higher in the minutes before the start of trading in New York. Brent crude oil moved up 0.5 percent from the previous close to $44.40 per barrel. West Texas Intermediate, the U.S. benchmark price for crude oil, was up in parallel to $41.98 per barrel.

Thursday's rally was supported in part by data from the European Union showing the annual inflation rate in March was flat, compared with a negative rate in February. The March 2015 rate of inflation was negative 0.1 percent.

A three-day rally for crude oil prices was snapped Wednesday when OPEC lowered its forecast for global oil demand growth by 50,000 barrels per day to 1.2 million bpd, an estimate that's 20 percent lower than the growth from last year. The IEA, however, said it was "confident" about demand momentum moving through 2016.

"We have not made changes to our demand numbers," it said.

While the anticipation ahead of the meetings in Doha has led to forward momentum for crude oil prices, some in the market are expecting a slow recovery. BP Chairman Carl-Henric Svanberg said at the company's annual shareholder meeting Thursday that oil prices will stay lower for longer, but not forever.

"Supply and demand should start to get back in balance as we go through the year and the oil price should respond positively," he said.