* Middle East tensions raise risk of supply disruptions
* But increase in U.S. oil drilling caps prices (Updates with comment, refreshes prices; changes dateline from SINGAPORE)
LONDON, Nov 13 (Reuters) - Oil was largely steady on Monday, trapped between a bullish push from tension in the Middle East and downward pressure from evidence of rising U.S. production, although record fund bets on a rally kept the price in sight of two-year highs.
Brent crude futures were down 17 cents at $63.35 a barrel by 1002 GMT, having gained 14 percent so far this month. U.S. West Texas Intermediate (WTI) crude eased 6 cents to $56.68.
Traders said crude prices were generally well supported as output cuts led by the Organization of the Petroleum Exporting Countries and Russia have contributed to a significant reduction in excess supplies that have dogged markets since 2014.
The excess of industrialized countries' oil stockpiles over their five-year average "has fallen by more than 50 percent in 2017, with inventories currently at around 160 million barrels," consultancy Timera Energy said.
"If current trends continue, inventories are likely to return to the five-year average at some stage in 2018," it said, adding that strong demand had also helped reduce the glut.
Hedge funds increased their holdings of Brent crude futures and options in the latest week, pushing their bet on a sustained rally in the oil price to the highest on record.
Money managers now hold a net long position in Brent futures and options equivalent to nearly 544 million barrels of oil.
"Overall, there are a few reasons for confidence - compliance from OPEC - and it seems likely they'll extend the cut," Jasper Lawler, a market strategist with London Capital Group, said.
On the supply side, tensions in the Middle East raised the prospect of disruptions, traders said, adding it was unclear whether a strong earthquake that hit Iran and Iraq on Sunday had affected the region's oil production.
Bahrain said over the weekend that an explosion that caused a fire at its main oil pipeline on Friday was caused by sabotage, linking the attack to Iran, which denied any role.
The rise in WTI futures towards $60 last week brought an increase in U.S. drilling. U.S. producers added nine oil rigs in the week to Nov. 10, the biggest jump since June, raising the count to 738, energy services firm Baker Hughes said on Friday.
The rig count <RIG-OL-USA-BHI> is also much higher than a year ago, when only 452 rigs were active, indicating that the U.S. oil industry is comfortable operating at current prices.
(Editing by Dale Hudson)