TOKYO/SINGAPORE (Reuters) - Oil fell on Thursday as weak U.S. economic data raised concerns over a potential global recession and demand reduction, but benchmark prices were headed for a weekly advance after OPEC+ announced further output cuts and U.S. oil stocks dropped.

Brent crude futures fell 74 cents, or 0.9%, to $84.25 a barrel by 0344 GMT. West Texas Intermediate U.S. crude slid 73 cents, also 0.9%, to $79.88 a barrel.

Brent and WTI have both gained more than 5.5% so far this week, headed towards three straight weeks of increase, after the Organization of the Petroleum Exporting Countries and allies including Russia, a grouping known as OPEC+, pledged voluntary production cuts.

"Crude oil's rally paused as it battled the headwinds created by the weak economic data. This offset more positive fundamentals," ANZ Research said in a note.

The U.S. services sector slowed more than expected in March as demand cooled, while a measure of prices paid by services businesses fell to the lowest in nearly three years, giving the Federal Reserve a boost in the fight against inflation.

New Zealand's central bank raised interest rates more than expected on Wednesday, and India is likely to be the next in line to step up its benchmark rates.

Meanwhile, U.S. job openings in February dropped to their lowest in nearly two years, suggesting the labour market was cooling. The slew of soft economic data soured market sentiment, stoking fears of a recession and prompting investors to adopt risk aversion strategies.

The U.S. dollar index strengthened on Thursday, rebounding from a recent two-month-low. A stronger greenback could dent oil demand as crude becomes more expensive for holders of other currencies.

"A slowdown in the U.S. economic outlook is weighing on the upside on U.S. oil prices, however we continue to expect a further uptick in oil prices to the end of the quarter," Baden Moore and Adam Skelton, analysts from National Australia Bank, wrote in a note.

Underpinning the market, Saudi Arabia, the world's top oil exporter, raised prices for its flagship crude for Asian buyers for a third straight month.

"This points to further strength in demand in the region," ANZ Research said.

U.S. crude inventories fell 3.7 million barrels last week, about 1.5 million barrels more than forecast, government data showed.

Gasoline and distillate stocks also fell more than expected, drawing down by 4.1 million barrels and 3.6 million barrels, respectively.