* Middle East tensions raise risk of supply disruptions
* But increase in U.S. oil drilling caps prices
By Henning Gloystein
SINGAPORE, Nov 13 (Reuters) - Oil markets opened the week cautiously on Monday amid ongoing tensions in the Middle East and after a rising rig count in the United States suggested producers there are preparing to increase output.
Brent crude futures were at $63.64 per barrel at 0049 GMT, up 12 cents from their last close.
U.S. West Texas Intermediate (WTI) crude was at $56.87 per barrel, up 13 cents from its last settlement.
Traders said crude prices were generally well supported as ongoing output cuts led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia have contributed to a significant reduction in excess supplies that have been dogging markets since 2014.
Tensions in the Middle East raised the prospects of supply disruptions, traders said.
Bahrain said over the weekend that an explosion which caused a fire at its main oil pipeline on Friday was caused by sabotage, linking the attack to Iran, which denied any role in the incident.
Despite the Middle East tensions and OPEC-led supply cuts, traders were cautious in betting on further price rises, not least because of an increase in U.S. drilling for new production.
U.S. drillers added nine oil rigs in the week to Nov. 10, the biggest jump since June, bringing the total count up to 738, General Electric Co's Baker Hughes energy services firm said late on Friday.
The rig count RIG-OL-USA-BHI, an early indicator of future output, 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 crude price levels.
U.S. oil producers have raised output C-OUT-T-EIA by more than 14 percent since mid-2016 to a record 9.62 million barrels per day.
This led to a slide in crude futures prices late on Friday away from over two-year highs reached early last week, traders said.
Reporting by Henning Gloystein; Editing by Joseph Radford