UPDATE 4-Oil steadies as drilling increases in tight market

* U.S. oil drilling increases

* U.S. inventories tight

* Concerns about impact of trade war fade (Updates prices and comment in paragraphs 2-3)

LONDON, July 9 (Reuters) - Oil prices steadied on Monday as an increase in U.S. drilling, likely to lead to higher shale production, balanced evidence of tightening supply.

Benchmark Brent was up 40 cents at $77.51 a barrel by 0850 GMT. U.S. crude was down 30 cents at $73.50.

"Uncertainties abound when it comes to the oil balance for the remainder of the year," said Stephen Brennock, analyst at London brokerage PVM Oil Associates. "Competing supply-side developments ensure that the oil price roller-coaster remains in full swing."

U.S. energy companies last week increased the number of rigs drilling for oil by five to 863, up 100 year-on-year, General Electric Co's Baker Hughes energy services firm said in its closely followed report late on Friday.

The U.S. rig count, an early indicator of future output, is much higher than a year ago as energy companies have ramped up production in response to higher prices.

Extra output is needed because oil demand has been rising fast this year and supply from several parts of the world, including Venezuela and Libya, has been falling.

This has tightened the market, especially in the United States.

Crude oil inventories at Cushing, Oklahoma, the delivery point for U.S. crude futures, have fallen to their lowest in 3-1/2 years, data showed last week.

"Cushing is clearly screaming out for crude," said Virendra Chauhan, oil analyst at Energy Aspects in Singapore.

The Organization of the Petroleum Exporting Countries and other countries 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.

Concerns that oil prices will be weighed down by a trade conflict between the United States and China have faded to some extent, analysts said.

The United States and China exchanged the first salvos in what could become a protracted trade war on Friday, slapping tariffs on $34 billion worth of each others' goods and giving no sign of willingness to start talks aimed at a reaching a truce.

(Additional reporting by Aaron Sheldrick in Tokyo; Editing by Mark Potter and Louise Heavens)