* Mideast geopolitical tensions continue to support prices
* OPEC sees oil markets tightening even as U.S. produces more
* OPEC's SecGen predicts market balance by Q2-Q3
* OPEC/Russia supply cuts set to be extended into 2019 (Recasts; updates prices, market activity and comments)
NEW YORK, April 12 (Reuters) - Oil prices held steady on Thursday, remaining close to highs last reached in late 2014 on Middle East geopolitical tensions and shrinking global oil inventories.
Brent crude futures were at $71.84 a barrel by 2:01 p.m. EDT (1801 GMT), down 22 cents. U.S. WTI crude futures were up 3 cents at $66.85. On Wednesday, both crude benchmarks hit their highest levels since late 2014.
Prices had started to pull back earlier in Thursday's session, pressured by a stronger dollar, but recovered as the dollar retreated.
A stronger greenback makes it more expensive to buy dollar-denominated commodities like oil
"It wasn't much of a pull back," said Walter Zimmerman, chief technical analyst at United-ICAP. "People are still nervous about what's going to happen in Syria...nothing was solved overnight," he said.
Oil prices jumped on Wednesday after Saudi Arabia said it intercepted missiles over Riyadh and U.S. President Donald Trump warned of military action in Syria, both of which raised concerns about possible supply disruptions.
Fundamental signals also supported prices. The Organization of the Petroleum Exporting Countries said the global oil stocks surplus was close to evaporating due to healthy demand and its own supply cuts.
The group is producing oil below its targets, meaning the world needs to use stocks to meet rising demand. OPEC said in its monthly report oil stocks in the developed world fell by 17.4 million barrels in February to 2.854 billion barrels, around 43 million barrels above the latest five-year average.
OPEC Secretary-General Mohammad Barkindo told Reuters in New Delhi the global oil glut has effectively shrunk by nine-tenths since the start of 2017.
"We have seen an accelerated shrinkage of stocks in storage from unparalleled highs of about 400 million barrels to about 43 million above the five-year average," Barkindo said.
OPEC, Russia and several other non-OPEC producers began trimming supply in January 2017. Their pact runs until the end of the year and OPEC meets in June to decide on its next course of action.
"There is growing confidence that the declaration of cooperation will be extended beyond 2018," Barkindo told Reuters. "Russia will continue to play a leading role."
These bullish factors more than offset pressure from a U.S. government report showing crude oil inventories <C-STK-T-EIA> rose by 3.3 million barrels, while domestic production <C-OUT-T-EIA> hit a record 10.53 million barrels per day (bpd).
(Additional reporting by Libby George and Dmitry Zhdannikov in London; Henning Gloystein in Singapore Editing by David Gregorio and David Evans)