* Climbing U.S. output pressures prices
* Middle East tensions limit price drops
* Facebook slide drags Wall Street stocks (New throughout, updates prices, market activity and comments; new byline, changes dateline, previous LONDON)
NEW YORK, March 19 (Reuters) - Oil prices slipped on Monday as Wall Street slid more than 1 percent and energy market investors remained wary of growing crude supply, although tensions between Saudi Arabia and Iran gave prices some support.
Brent crude futures were down 34 cents at $65.87 a barrel by 11:35 a.m. EST (1535 GMT). U.S. West Texas Intermediate (WTI) futures fell 52 cents to $61.82 a barrel. Both contracts had risen briefly in early trade.
"The equity markets are certainly a driving factor behind this slide today," said Brian LaRose, technical analyst at United-ICAP in Jersey City, New Jersey. "Since the open, they have been hit pretty hard," he said.
Wall Street's main indexes fell 1 percent as investors worried about a potential trade war and as tumbling Facebook shares dragged the tech sector. Oil prices have been increasingly moving in tandem with equities.
A rise in U.S. rig counts last week also weighed on crude prices. U.S. drillers added four oil rigs in the week to March 16, bringing the total count to 800, the weekly Baker Hughes drilling report said on Friday.
"At the current oil price level, drilling activity and thus output in the U.S. is likely to increase further," analysts at Commerzbank said in a note.
The U.S. rig count, an early indicator of future output, is much higher than a year ago as energy firms have boosted spending. Consequently, U.S. crude oil production <C-OUT-T-EIA> has risen more than a fifth since mid-2016, to 10.38 million barrels per day (bpd), pushing the United States past top exporter Saudi Arabia. Oil did get some price some support from geopolitical tensions. Prices climbed on Friday after Saudi Crown Prince Mohammed bin Salman said the kingdom would develop nuclear weapons if arch-rival Iran did.
"This week there will be ... a pricing of some geopolitical risk with the crown prince going on a visit to the United States which is likely to provide a lot of headlines against Iran and the ... deal," Petromatrix analyst Olivier Jakob said, referring to Iran's pact that has removed sanctions on that country in return for limits on its nuclear program.
President Donald Trump has told European powers they must "fix the terrible flaws" in the deal or the United States would stop its sanctions relief.
Britain, France and Germany have proposed fresh European Union sanctions on Iran over its ballistic missiles program and its role in Syria's war, Reuters reported.
(Additional reporting by Ahmad Ghaddar and Tom Balmforth in London; Henning Gloystein in Singapore Editing by Edmund Blair and David Gregorio)