* Concern that U.S. may bring back sanctions against Iran
* Shanghai crude repeats high launch-day trading volumes
* Surging U.S. output looms over otherwise bullish market (Adds comment on U.S. output, updates prices)
SINGAPORE, March 27 (Reuters) - Oil prices rose on Tuesday, pushed up by concerns that tensions in the Middle East could lead to supply disruptions.
Hopes that behind-the-scenes talks between the United States and China will prevent a looming trade war between the world's two biggest economies also supported global markets, including crude oil futures.
U.S. West Texas Intermediate (WTI) crude futures were at $65.89 a barrel at 0407 GMT, up 34 cents, or 0.5 percent, from their previous close.
Brent crude futures were at $70.34 per barrel, up 22 cents, or 0.3 percent.
James Mick, Managing Director and Energy Portfolio Manager with asset management firm Tortoise, said "rising geopolitical tensions" were driving up oil prices. The biggest risk was that the United States could re-introduce sanctions on Iran.
"Crude also received support from OPEC members as Saudi Arabia and Russia both reiterated goals to extend the production cut agreement," Mick said.
Iraq, the second biggest producer within the Organization of the Petroleum Exporting Countries (OPEC) said on Monday that it also supports the producer cartel's agreement to cut oil output.
OPEC, together with a group of non-OPEC producers led by Russia, started withholding production in 2017 in order to prop up prices. The deal to cut is scheduled to last through 2018, and there has been recent support by OPEC's de-facto leader Saudi Arabia to extend the cuts into 2019.
However, some traders cautioned that such a moved faced opposition.
Stephen Innes, head of trading for Asia/Pacific at futures brokerage OANDA in Singapore said there was "considerable resistance" as current or higher prices opened the possibility that even more U.S. shale producers could come back online.
U.S. oil production has already jumped by almost a quarter since mid-2016, to 10.4 million barrels per day (bpd) <C-OUT-T-EIA>, taking it past top exporter Saudi Arabia and within reach of top producer Russia, which pumps around 11 million bpd.
Singapore-based brokerage Phillip Futures said "surging production levels persist" in the United States.
In Asia, Shanghai crude oil futures saw their second day of trading, repeating Monday's high volumes.
Over the first 24 hours of its trading, Shanghai's spot crude volumes made up 5 percent of the global market, versus 23 percent for Brent and 72 percent for WTI.
Brent volumes are currently low as much of Europe is already on holidays for Easter.
Shanghai crude fell 1.4 percent from the overnight settlement of 433.8 yuan ($69.33) per barrel to 427.6 yuan ($68.34) at 0409 GMT on Tuesday.
In dollar-terms, Chinese crude prices are trading between Brent and WTI. ($1 = 6.2570 Chinese yuan renminbi)
(Reporting by Henning Gloystein; editing by Richard Pullin)