* OPEC+ could extend supply cuts beyond June, sources say

* Upcoming: U.S. oil and gas weekly rig count

May 3 (Reuters) - Oil prices edged up in early trade on Friday on the prospect of OPEC+ continuing output cuts, but the crude benchmarks were headed for weekly losses on U.S. economic uncertainty and limited crude supply disruptions caused by the Israel-Hamas war.

Brent crude futures for July rose 16 cents to $83.83 a barrel by 0008 GMT. U.S. West Texas Intermediate crude for June was up 19 cents to $79.14 per barrel.

Still, both benchmarks were on track for weekly losses as investors worried about the prospect of higher-for-longer interest rates curbing growth in the U.S., the top global oil consumer, while the war in the Middle East showed little sign of disrupting global oil supplies.

Brent headed for a 6.3% weekly decline, while and WTI moved towards a loss of 5.6% on the week.

The drop comes just weeks ahead of the next meeting of the Organization of the Petroleum Exporting Countries and allies led by Russia, together called OPEC+.

Three sources from OPEC+ producers said the group could extend its voluntary oil output cuts of 2.2 million barrels per day beyond June if oil demand fails to pick up, but the group has yet to begin formal talks ahead of the June 1 meeting.

The market is now looking towards U.S. economic data and indicators of future crude supply from the world's top producer.

On Friday, the U.S. Bureau of Labor Statistics releases its monthly nonfarm payroll report, which is a measure of the strength of the country's job market and is considered by the Federal Reserve when setting interest rates. Higher rates typically weigh on the economy and that can reduce oil demand.

Also on Friday, energy services firm Baker Hughes is due to release its weekly count of oil and gas rigs, an indicator of future crude output.

(Reporting by Laila Kearney in New York; Editing by Sonali Paul)