* U.N. Libya envoy says Haftar made coup attempt
* Iran's oil exports hit new 2019 low so far in April - sources
* Russia's Gazprom Neft sees global oil deal ending in mid-2019
* U.S. crude oil stocks fall unexpectedly, down 3.1 mln bbls -API (Updates with API data on U.S. crude inventories)
By Stephanie Kelly
NEW YORK, April 16 (Reuters) - Oil prices rose 1 percent on Tuesday, as fighting in Libya and falling Venezuelan and Iranian exports raised concerns over tightening global supply, but uncertainty surrounding an OPEC-led production cut limited gains.
Brent crude futures rose 54 cents, or 0.8 percent, to settle at $71.72 a barrel. U.S. West Texas Intermediate (WTI) crude futures gained 65 cents, or 1 percent, to settle at $64.05 a barrel.
Prices extended gains in post-settlement trade after data from industry group the American Petroleum Institute showed that U.S. crude inventories fell unexpectedly last week, dropping by 3.1 million barrels, versus analysts' expectations of a 1.7 million-barrel build.
Gasoline stockpiles fell by 3.6 million barrels, the API said, more than forecasts of a 2.1 million-barrel drop.
U.S. government data is due to be released Wednesday.
In Libya, fighting between Khalifa Haftar's Libyan National Army and the internationally recognized government has raised the prospect of lower supplies from the OPEC member.
U.S. sanctions on two other members, Iran and Venezuela, are already cutting shipments. Iran's crude oil exports have dropped in April to their lowest daily level this year, tanker data showed and industry sources said.
"Global supply is falling faster than people think. The market is imbalanced," said Phil Flynn, an analyst at Price Futures Group in Chicago. "The continuing loss of Venezuelan oil is going to take its toll. The OPEC cuts are going to take their toll."
Adding downward pressure, however, were concerns about Russia's willingness to stick with OPEC-led supply cuts and expectations of higher U.S. inventories.
Oil prices have gained this year more than 30 percent, helped by the deal between the Organization of the Petroleum Exporting Countries and other producers including Russia. The group has been cutting output since Jan. 1 and will decide in June whether to continue the arrangement.
Gazprom Neft, the oil arm of Russian gas giant Gazprom, expects the global oil deal between OPEC and its allies to end in the first half of the year, a company official said on Tuesday.
Russia and the producer group may decide to boost output to fight for market share with the United States, TASS news agency сited Finance Minister Anton Siluanov as saying on Saturday.
"There is a growing concern that Russia will not agree on extending production cuts and we could see them officially abandon it in the coming months," said Edward Moya, senior market analyst at OANDA.
Reporting by Stephanie Kelly; additional reporting by Alex Lawler in London Editing by Marguerita Choy and Richard Chang