* Islamic State extends gains in north, at Kurdish border post
* NY Times says Obama weighing airstrikes, White House cautious
* France, Pope urge international action to stop Islamists
* Residents flee biggest Christian town
* U.S. oil majors evacuate staff from Kurdish area
(Adds French, NYT report on U.S. options, oil majors evacuate)
ARBIL, Iraq, Aug 7 (Reuters) - Islamist militants surged across northern Iraq towards the capital of the Kurdish region on Thursday, sending tens of thousands of Christians fleeing for their lives, in an offensive that sparked talk of Western military action.
Reuters photographs showed what appeared to be Islamic State fighters controlling a checkpoint at the border area of the Kurdish semi-autonomous region, little over 30 minutes' drive from Arbil, a city of 1.5 million that is headquarters to the Kurdish regional government and of many businesses.
The fighters had raised the movement's black flag over the guard post. However a Kurdish security official denied that the militants were in control of the Khazer checkpoint, and the regional government said its forces were advancing and would "defeat the terrorists", urging people to stay calm.
The New York Times reported that U.S. President Barack Obama was considering airstrikes or humanitarian airdrops to help trapped religious minorities in Iraq.
The White House said the U.S. government and military were supporting Iraqi and Kurdish forces to protect people trapped by Islamic State fighters.
Spokesman Josh Earnest said any U.S. military action would be "very limited in scope" and tied to Iraqi political reforms, adding: "There are no American military solutions to the problems in Iraq."
Sunni militants captured Iraq's biggest Christian town, Qaraqosh, prompting many residents to flee, fearing they would be subjected to the same demands the Sunni militants made in other captured areas - leave, convert to Islam or face death.
The Islamic State, considered more extreme than al-Qaeda, sees Iraq's majority Shi'ites and minorities such as Christians and Yazidis, a Kurdish ethno-religious community, as infidels.
France called for an emergency meeting of the U.N. Security Council to "counter the terrorist threat in Iraq".
President Francois Hollande's office said after he spoke by telephone with Kurdistan president Masoud Barzani that Paris was prepared to support forces engaged in the defence of Iraqi Kurdistan. It did not say how.
Shares in energy companies operating in Iraqi Kurdistan plummeted on news of the sweeping Islamist advance towards oilfields in the region.
U.S. oil major Chevron Corp said it was evacuating staff in light of the militants' advance, and an industry source said Exxon Mobil Corp was also pulling out staff, although the company declined comment on security concerns.
The Islamic State said in a statement on its Twitter account that its fighters had seized 15 towns, the strategic Mosul dam on the Tigris River and a military base, in an ongoing offensive that began at the weekend.
Kurdish officials say their forces still control the dam, Iraq's biggest.
On Thursday, two witnesses told Reuters by telephone that Islamic State fighters had hoisted the group's black flag over the dam, which could allow the militants to flood major cities or cut off significant water supplies and electricity.
The Sunni militants inflicted a humiliating defeat on Kurdish forces in the weekend sweep, prompting tens of thousands from the ancient Yazidi community to flee the town of Sinjar for surrounding mountains.
BOMBINGS ACROSS IRAQ
Facebook and Twitter were blocked in Kurdistan on Thursday, initially for 24 hours. A government official told Reuters the reason was to prevent militants from gathering any information about the movement of Kurdish forces from social media, and to stop rumours and panic.
The Kurdish Regional government's Ministry of Interior said in a statement that "our victory is close".
A Kurdish government security adviser said the were multiple layers of security and a trench protecting the regional capital. "Arbil city is fine," he said.
The militants' weekend capture of the town of Sinjar, ancestral home of the Yazidi ethnic minority, prompted tens of thousands of people to flee to surrounding mountains, where they are at risk of starvation.
Some of the many thousands trapped on Sinjar mountain have been rescued in the past 24 hours, a spokesman for the U.N. Office for the Coordination of Humanitarian Affairs said, adding that 200,000 had fled the fighting.
"This is a tragedy of immense proportions, impacting the lives of hundreds of thousands of people," spokesman David Swanson said by telephone.
Many of the displaced people urgently need water, food, shelter and medicine, he said. A spokesman for the U.N. agency for children said many of the children on the mountain were suffering from dehydration and at least 40 had died.
Yazidis, seen by the Islamic State as "devil worshipers", risk being executed by the Sunni militants seeking to establish an Islamic empire and redraw the map of the Middle East.
Thousands of Iraqis, most of the Yazidis, are streaming to the border with neighbouring Turkey to flee the fighting, Turkish officials said.
The plight of fleeing Christians prompted Pope Francis to appeal to world leaders to help end what the Vatican called "the humanitarian tragedy now under way" in northern Iraq.
In Kirkuk, a strategic oil town in the north held by Kurdish forces since government troops melted away in June, 11 people were killed by two car bombs that exploded near a Shi'ite mosque holding displaced people, security and medical sources said.
In Baghdad, a suicide bomber blew himself up in a Shi'ite district, killing at least six people, police said. Earlier, a car bomb in another Shi'ite area of the capital killed 14.
Gains by the Islamic State have raised concerns that militants across the Arab world will follow their cue. At the weekend the Sunni militants seized a border town in Lebanon, though they appear to have mostly withdrawn.
The Islamic State, which has declared a caliphate in the areas of Iraq and Syria it controls, clashed with Kurdish forces on Wednesday in the town of Makhmur, about 40 miles southwest of Arbil, the capital of the Kurdish autonomous zone.
Witnesses said the militants had seized Makhmur, but Kurdish officials told local media their forces remained in control there, and television channels broadcast footage of Kurdish peshmerga fighters driving around the town.
The mainly Christian town of Tilkaif, as well as Al Kwair, were overrun by militants, according to witnesses.
THREAT TO IRAQ'S INTEGRITY
The Islamic State poses the biggest threat to Iraq's integrity since the fall of Saddam Hussein in 2003. Its fighters and their Sunni allies also control a big chunk of western Iraq.
The group has deepened sectarian tensions, pushing the country back to the dark days of the civil war that peaked in 2006-2007 under U.S.-led occupation.
Bombings, kidnappings and executions are routine once again in Iraq, an OPEC member. Religious and ethnic minorities that have lived in the plains of the northern province of Nineveh are particularly vulnerable.
Sunni militants have been purging Shi'ite Muslims of the Shabak and ethnic Turkmen minorities from towns and villages in Nineveh, and last month set a deadline for Christians to leave the provincial capital Mosul or be killed.
The Islamic State's gains have prompted Iraqi Prime Minister Nuri al-Maliki, a Shi'ite, to order his airforce to help the Kurds, whose reputation as fearsome warriors was called into question by their defeat.
There were several airforce strikes on Wednesday, including one the government said killed 60 "terrorists" in Mosul, but they did not appear to have broken the Islamic State's momentum.
(Additional reporting by Tom Miles in Geneva and James Mackenzie in Rome; Writing by Michael Georgy; Editing by Paul Taylor, Janet McBride and Will Waterman)