Oil prices edged lower on Tuesday, giving up most of the prior session's gains that followed an announcement by the world's top exporter, Saudi Arabia, that it would further cut output.

Brent crude futures were down 23 cents, or 0.3%, at $76.48 a barrel at 0020 GMT. The U.S. West Texas Intermediate crude eased 25 cents, or 0.4%, to $71.90 a barrel.

Brent had gained as much as $2.6 on Monday and U.S. crude had risen as much as $3.3 in the hours after Saudi Arabia said its output would drop by 1 million barrels per day (bpd) to 9 million bpd in July.

The voluntary cut, Saudi Arabia's biggest in years, is on top of a broader deal by the Organization of the Petroleum Exporting Countries (OPEC) and allies including Russia to limit supply into 2024 as OPEC+ seeks to boost flagging oil prices.

The OPEC+ pumps around 40% of the world's crude.

However, many of these reductions announced after the OPEC meeting in Vienna on Sunday may not have a real impact as the group lowered the targets for Russia, Nigeria, and Angola to bring them into line with actual current production levels.

Market participants are now waiting to see if the U.S. Federal Reserve will hike or hold interest rates in June for more trading cues. Higher rates could curb energy demand.

Data on Monday that showed that the U.S. services sector barely grew in May as new orders slowed fuelled hopes that the Fed will refrain from raising rates.

Traders pegged the chances of the Fed pausing its interest rate hikes at its June 13-14 meeting at 78%, according to the CME FedWatch Tool.

European Central Bank President Christine Lagarde on Monday acknowledged "signs of moderation" in core inflation in the euro zone but reaffirmed it was too early to call a peak in that key gauge of price growth, increasing expectations for more interest rate increases from the ECB this month and the next. (Reporting by Arathy Somasekhar in Houston; Editing by Himani Sarkar)