* Geopolitics not fundamentals lift prices - analyst
* Relentless rise in U.S. crude output caps gains
* Economic crisis halves Venezuelan output since 2005 (Updates with comment, refreshes prices. Changes dateline from SINGAPORE)
LONDON, March 20 (Reuters) - Oil rose on Tuesday to its highest level so far this month, lifted by tension in the Middle East and the possibility of further falls in Venezuelan output.
Brent futures were up 70 cents at $66.75 a barrel by 1027 GMT, after hitting $66.79, the highest level since late February. U.S. West Texas Intermediate (WTI) crude futures were up 45 cents at $62.51 a barrel.
"The move today is more to do with geopolitical tensions than underlying fundamentals, but I don't expect that to last," PVM Oil Associates strategist Tamas Varga said.
Saudi Arabia called the 2015 nuclear deal between Iran and world powers a "flawed agreement" on Monday, on the eve of a meeting between the Saudi crown prince and U.S. President Donald Trump. Both are highly critical of Iran.
Trump has threatened to withdraw the United States from the accord between Tehran and six world powers, raising the prospect of new sanctions that could hurt Iran's oil industry.
"Tensions between Saudi Arabia and Iran gave prices some support," Sukrit Vijayakar, director of energy consultancy Trifecta, said in a note.
Worries about falling production in Venezuela, whose output has been halved since 2005 to below 2 million barrels per day (bpd) <PRODN-VE> due to an economic crisis, also supported oil markets.
The International Energy Agency said last week Venezuela was "vulnerable to an accelerated decline" and such a disruption could tip global markets into deficit.
PVM's Varga said Venezuela was a potential source of supply disruption, but he said the bigger challenge for OPEC and its allies was ensuring their efforts to balance the market through output curbs was not undermined by rising production elsewhere.
Output has climbed sharply in the United States, Canada and Brazil, as they ramp up production to benefit from higher crude prices that have been buoyed by the cuts made by the Organization of the Petroleum Exporting Countries, Russia and their allies. The production rise has capped oil price gains.
Appetite for U.S. crude is adding to the headache facing OPEC. A widening discount of WTI to Brent crude makes it more attractive for foreign refiners to process U.S. oil. Brent is the benchmark for several Middle East and other global crudes.
"Spot Brent crude oil prices averaged $3.36 per barrel more than WTI prices in 2017 compared with just $0.40 per barrel more in 2016, providing a price incentive to export U.S. crude oil into the international market," said Matt Stanley, a fuel broker at Freight Investor Services International in a note.
The premium of Brent crude to WTI rose above $4 a barrel on Tuesday, its widest in a month.
(Additional reporting by Henning Gloystein in Singapore Editing by Edmund Blair)