* Sunni Islamists strengthen grip on northern Iraq
* Crude oil flow from Iraqi Kurdistan continues
* Iraqi government secures oilfields
* Kurds demand 25 pct of oil revenues (Updates prices to settlement)
By Anna Louie Sussman
NEW YORK, June 16 (Reuters) - Brent crude oil futures rose on Monday as advances by Sunni insurgents in Iraq fueled concerns over a potential disruption to oil exports from OPEC's second-largest producer.
Brent's increase extended last week's gains of more than 4 percent, the most since July, which were sparked by the eruption of violence in Iraq.
The rally lost some steam on Monday as the Iraqi government tightened security and deployed extra troops around oil infrastructure and oilfields to help protect its vital energy industry from Sunni Muslim insurgents who have gained ground over the past week, according to a senior Iraqi security official.
U.S. crude oil futures fell, as traders booked profits after oil futures hit a session high of $107.54. Surging domestic oil production in the U.S. makes it less vulnerable than other countries to a supply squeeze out of Iraq.
"U.S. crude is going to have a muted response, because we're more independent than we were in the past," said Mark Waggoner, president of Excel Futures in Bend, Oregon.
Brent crude for August delivery rose by 48 cents to settle at $112.94 a barrel, 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 fell by 1 cent to $106.90 a barrel, after swinging by nearly $1, between $106.61 and $107.54. The U.S. July contract expires on June 20.
The spread between the two August benchmarks CL-LCO1=R widened out to $6.72, after earlier narrowing to $5.99.
U.S. Secretary of State John Kerry said the United States was considering air strikes to help the Iraqi government fend off the insurgency, but would not coordinate military action with Iran.
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.
The Kurdistan Regional Government believes its share of total Iraqi oil sales should be as high as 25 percent, up from a current 17 percent, the KRG's official spokesman said on Monday.
Should the militants advance south of Baghdad, the capital, analysts expect them to encounter much greater resistance in the largely Shi'ite south.
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 Robert Gibbons in New York, Claire Milhench in London and Jacob Gronholt-Pedersen in Singapore; Editing by Jason Neely, Dale Hudson, Marguerita Choy, Meredith Mazzilli and Chizu Nomiyama)