* OPEC, allies extend output curbs until March 2020
* Slowing global economy seen sapping oil demand
* U.S., China agreed to restart trade talks at G20
* Coming up: API data on U.S. crude stocks at 4:30 p.m. EDT (Updates prices, market activity, adds commentary)
NEW YORK, July 2 (Reuters) - Oil prices fell more than 4% on Tuesday, even after OPEC and allies including Russia agreed to extend supply cuts until next March, as weak manufacturing data had investors worried that a slowing global economy could dent oil demand.
Brent crude futures fell $2.66, or 4.1%, to settle at $62.40 a barrel. U.S. West Texas Intermediate (WTI) crude futures fell $2.84, or 4.8%, to settle at $56.25 a barrel, after touching their highest in more than five weeks on Monday.
The Organization of the Petroleum Exporting Countries and other producers such as Russia, a group known as OPEC+, agreed on Tuesday to extend oil supply cuts until March 2020 as members overcame differences to try to prop up prices.
The extension comes after Russian President Vladimir Putin said on Saturday he had agreed with Saudi Arabia to prolong the pact and continue to cut combined production by 1.2 million barrels per day, or 1.2% of world demand.
Signs of a global economic slowdown, which could hit oil demand growth, means OPEC and its allies could face an uphill battle to shore up prices by reining in supply.
"It was the bare minimum OPEC could agree on in order to prevent a major meltdown in prices. Member countries noted that global oil demand growth for this year has fallen to 1.14 mbpd (million barrels per day) whilst non-OPEC supply is expected to grow by 2.14 mbpd," PVM analyst Tamas Varga wrote in a note.
"It appears that the supply side of the oil equation is supportive for oil prices but demand concerns are forcing oil bulls to keep at least part of their gunpowder dry."
The United States and China agreed at the G20 summit to restart trade talks, but factory activity shrank across much of Europe and Asia in June while U.S. manufacturing activity slowed to near a three-year low.
Further, U.S. President Donald Trump on Monday said any deal would need to be somewhat tilted in favor of the United States, which stoked doubt over prospects for a trade deal between the top two economies.
"Increasing indications of global economic slowing remain as the larger negative pricing consideration to the energy complex and OPEC's need to extend production cuts even further would appear to attest to slowing economic growth paths," Jim Ritterbusch of Ritterbusch and Associates said in a note.
Meanwhile, U.S. crude oil stockpiles were seen falling for a third consecutive week, a preliminary Reuters poll showed. Industry data will be released at 4:30 p.m. EDT (2030 GMT), with government data to follow on Wednesday. (Reporting by Stephanie Kelly; Additional reporting by Noah Browning in London and Jessica Jaganathan in Singapore; Editing by Diane Craft and Lisa Shumaker)