UPDATE 6-Oil prices climb on global demand, U.S. sanctions on Iran

* 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 tight (Updates prices, comment in paragraphs 2-3)

LONDON, July 9 (Reuters) - Oil prices rose on Monday as increased global demand and U.S. efforts to shut out Iranian output using sanctions outweighed drilling data suggesting U.S. shale production would climb.

Benchmark Brent was up 70 cents at $77.81 a barrel by 1150 GMT. U.S. crude was unchanged at $73.80.

"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 oil 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 have little spare capacity and oil demand has risen faster than supply over the last year.

At the same time, exports from several OPEC producers, including Venezuela and Libya, have been falling.

"If the Saudis and others replace the losses from Iran, there will be basically no spare capacity left," Societe Generale 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 are successful in blocking Iranian exports.

U.S. energy companies last week increased the number of rigs drilling for oil by five to 863, up 100 year-on-year, Baker Hughes energy services firm said on Friday.

The U.S. rig count, an early indicator of future output, is much higher than a year ago as 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 show.

"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, which 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.

The tightness at Cushing and the potential increase in Gulf exports "both have implications for how quickly the prompt overhang in the market can clear, and thus provide some direction for prices", Chauhan said.

(Additional reporting by Aaron Sheldrick in Tokyo Editing by Louise Heavens and Edmund Blair)