* Sunni Islamists intensify grip on northern Iraq
* Crude oil flow from Iraqi Kurdistan continues
* Brent, U.S. crude add to last week's strong gains
(Rewrites, adds analyst comment, updates prices, moves dateline from previous LONDON)
NEW YORK, June 16 (Reuters) - Crude oil futures pushed higher in choppy trading on Monday as advances by Sunni insurgents in Iraq fueled concerns over a potential disruption to oil exports from the second-largest OPEC producer.
Both Brent and U.S. crude added to last week's gains of more than 4 percent, the most since July and December, respectively, sparked by the eruption of violence in Iraq.
The rally lost some steam on Monday as the market waited to see if crude oil exports would be affected and whether the United States would intervene to support the Iraqi government.
U.S. Secretary of State John Kerry said the United States was considering air strikes to help the Iraqi government fend off the insurgency, as well as possible discussions with Iran.
"Kerry's comments confirmed the notion that plans are being readied to assist the Maliki government to hold Baghdad and the south," said John Kilduff, partner at Again Capital LLC in New York.
"Oil prices definitely keyed off Kerry's remarks," he added.
Brent crude for August delivery was up 17 cents at $112.63 a barrel at 10:49 a.m. EDT (1449 GMT), after touching an intraday high of $113.28. The July contract, which expired on Friday, went off the board at $113.41 per barrel, the highest settlement since September 2013.
U.S. July crude was up 13 cents at $107.04 a barrel, after reaching $107.54 intraday, just below Friday's peak of $107.68. The U.S. July contract expires on June 20.
"We've had the initial shock, now we need to see what sort of response there will be from the Iraqis and how successful they will be in containing this," said Ole Hansen, senior commodity strategist at Saxo Bank. "The rally now needs to be supported by real concerns about supply."
EXPORTS SAFE FOR NOW
On Sunday, Sunni insurgents seized a mainly ethnic Turkmen city in northwestern Iraq after heavy fighting, intensifying their grip on the north.
Analysts and oil market participants await any sign of a threat to Iraq's oil supplies, most of which are hundreds of kilometers south of the fighting. Northern exports have run at a trickle for months, and few had expected a rapid recovery.
Should the militants advance south of Baghdad, the capital, analysts expect them to encounter much greater resistance.
"If the U.S. gets involved militarily to suppress the insurgents then I would expect the price of oil to start to recede," Dominick Chirichella, an analyst at the Energy Management Institute, said in a note.
Meanwhile, a third export cargo of piped oil from Iraqi Kurdistan is scheduled to depart Turkey's Mediterranean port of Ceyhan on June 22, and crude oil from Iraqi Kurdistan is flowing as normal.
(Additional reporting by Claire Milhench in London and Jacob Gronholt-Pedersen in Singapore; Editing by Jason Neely, Dale Hudson and Marguerita Choy)