* U.S. sanctions on Iran set to prevent some oil exports
* Limited spare capacity to fill gap in production
* U.S. oil drilling increases but U.S. inventories remain tight (Updates detail and prices; paragraphs 2, 7)
LONDON, July 9 (Reuters) - Oil prices rose on Monday as increased global demand and U.S. efforts to shut out Iranian output through the use of sanctions outweighed drilling data suggesting that U.S. shale production would climb.
Benchmark Brent crude oil was up 60 cents at $77.71 a barrel by 1330 GMT. U.S. light crude rose 10 cents to $73.90.
"Oil prices are starting the week on the front foot in anticipation of reduced supplies from Iran after U.S. sanctions," said Stephen Brennock, analyst at London brokerage PVM Oil Associates.
The United States says it wants to reduce oil exports from Iran, the world's fifth-biggest producer, to zero by November in a move that will oblige other big producers such as Saudi Arabia to pump more.
But Saudi Arabia and other members of the Organization of the Petroleum Exporting Countries (OPEC) have little spare capacity and oil demand has risen faster than supply over the past year.
At the same time there has been a decline in exports from several OPEC producers, including Libya.
Libya's national oil output has fallen to 527,000 barrels per day (bpd) from a high of 1.28 million bpd in February, the head of the National Oil Corporation said on Monday.
"If the Saudis and others replace the losses from Iran, there will be basically no spare capacity left," Societe Generale oil analyst Michael Wittner said.
U.S. oil output is increasing but is unlikely to be able to fill the supply gap if U.S. sanctions successfully block Iranian exports.
American energy companies last week increased the number of rigs drilling for oil by five to 863, up 100 year on year, energy services company Baker Hughes said on Friday.
The U.S. rig count, an early indicator of future output, is much higher than a year ago because companies have ramped up production in response to higher prices.
But the U.S. oil market is still tightening. Crude inventories at Cushing, Oklahoma, the delivery point for U.S. crude futures, have fallen to their lowest in 3-1/2 years, data shows.
"Cushing is clearly screaming out for crude," said Virendra Chauhan, oil analyst at consultancy Energy Aspects.
OPEC, Russia and other producers agreed in June to a modest increase in output to dampen oil prices that recently hit 3-1/2 year highs.
A rise in supply will reverse some of the output cuts that OPEC and other major producers put in place in early 2017 to end several years of glut.
(Additional reporting by Aaron Sheldrick in Tokyo Editing by Edmund Blair and David Goodman)