* Sunni Islamists solidify grip on northern Iraq
* Little immediate threat seen to Iraqi oil exports
* Crude oil flow from Iraqi Kurdistan continues
(Updates prices, adds Kerry comments)
LONDON, June 16 (Reuters) - Brent crude held above $112 a barrel on Monday after a strong rally last week, as advances by Sunni insurgents in Iraq raised concerns over a potential disruption to oil exports from the second-largest OPEC producer.
The eruption of violence in Iraq led to a spike in prices last week, with Brent and U.S. crude gaining more than 4 percent - the most since July and December, respectively.
But the rally seemed to run out of steam on Monday as the market waited to see how far 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.
"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."
Brent crude for August delivery was up 4 cents at $112.50 a barrel by 1342 GMT, after touching an intraday high of $113.28. The July contract, which expired on Friday, settled 39 cents higher at $113.41 per barrel, the highest settlement since September 2013.
U.S. oil was up 10 cents at $107.01 a barrel, after reaching an intraday high of $107.54 in Asian trading. On Friday, it rose as high as $107.68 before settling up 38 cents at $106.91.
Reflecting on Monday's more modest gains, oil futures brokers and analysts said it looked as if the move up last week had been overcooked.
"There seem to be some grounds for thinking that the government in Baghdad may be able to restrict the ... civil war," one said. "But while the Kirkuk-Ceyhan pipeline is out of action I don't think we will see prices fall much more."
Carsten Fritsch, an oil analyst at Commerzbank in Frankfurt, said in a note: "Brent should correct the lion's share of its latest price rise."
"Nonetheless, the threat of civil war ... does justify a risk premium given that the anticipated growth in Iraqi oil production may fail to materialise on account of the unstable security situation and an unwillingness to invest as a result."
EXPORTS SAFE FOR NOW
On Sunday, Sunni insurgents seized a mainly ethnic Turkmen city in northwestern Iraq after heavy fighting, solidifying their grip on the north.
For the moment the immediate threat to Iraq's oil supplies - most of which are hundreds of kilometres south of the fighting - remains limited, analysts and consultants say. Northern exports have run at a trickle for months, and few had expected a rapid recovery.
Should the militants advance south of 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 Jacob Gronholt-Pedersen in Singapore; Editing by Jason Neely and Dale Hudson)