* Ayatollah Sistani urges followers to fight Sunni insurgents
* ISIL advances into Diyala province near Iran border
* Obama mulls military options, will not send combat troops
* Global oil price surges, ISIL surrounds biggest refinery (Adds quotes from counterterrorism official, Obama critics)
By Raheem Salman and Isra al-Rubei'i
BAGHDAD, June 13 (Reuters) - Iraq's most senior Shi'ite Muslim cleric urged followers to take up arms against a full-blown Sunni militant insurgency to topple Shi'ite Prime Minister Nuri al-Maliki, a conflict that threatens civil war and a possible break-up of the country.
In Washington, U.S. President Barack Obama said he was reviewing military options, short of sending combat troops, to help Iraq fight the insurgency but warned any U.S. action must be accompanied by an Iraqi effort to bridge political divisions.
In a rare intervention at Friday prayers in the holy city of Kerbala, a message from Grand Ayatollah Ali al-Sistani, who is the highest religious authority for Shi'ites in Iraq, said people should unite to fight back against a lightning advance by militants from the radical Islamic State of Iraq and the Levant.
Fighters under the black flag of ISIL are sweeping south towards the capital Baghdad in a campaign to recreate a mediaeval caliphate carved out of fragmenting Iraq and Syria that has turned into a widespread rebellion against Maliki.
"People who are capable of carrying arms and fighting the terrorists in defence of their country ... should volunteer to join the security forces to achieve this sacred goal," said Sheikh Abdulmehdi al-Karbalai, delivering Sistani's message.
Those killed fighting ISIL militants would be martyrs, he said as the faithful chanted in acknowledgement.
Amidst the spreading chaos, Iraqi Kurdish forces seized control of Kirkuk, an oil hub just outside their autonomous enclave that they have long seen as their historical capital, three days after ISIL fighters captured the major city of Mosul.
There are concerns that sectarian and tribal conflict might dismember Iraq into Shi'ite, Sunni and Kurdish entities. The atmosphere in Baghdad was tense on Friday, the streets were empty, residents were stock-piling food and arming themselves.
Reflecting fears that ISIL's insurgency could erupt into a civil war and disrupt oil exports from a major OPEC member state, the price of Brent crude oil edged further above $113 a barrel on Friday, up about $4 since the start of the week.
MALIKI MUST ACT
Obama told reporters at the White House he would not send U.S. troops back into combat in Iraq but had asked his national security team to prepare "a range of other options" to help Iraqi security forces confront fighters from ISIL. He made clear he expected steps toward Iraqi political reconciliation.
"The United States is not simply going involve itself in a military action in the absence of a political plan by the Iraqis that gives us some assurance that they are prepared to work together," he said.
The U.S. president was facing a chorus of criticism from Republican opponents who say that his missteps in responding to the Syrian civil war and dithering on Iraq has left the United States with few options.
"We need to be hitting these columns of terrorists marching on Baghdad with drones now," said Representative Ed Royce, the chairman of the House Foreign Affairs Committee. Influential Senators John McCain and Lindsey Graham also called for air strikes to deal the insurgents "a crippling blow."
American officials have watched in dismay as the U.S.-trained and -armed Iraqi security forces have crumbled and fled in the face of an onslaught by the militants. Obama noted the United States had invested a lot of money and training in the Iraqi security forces.
"The fact that they are not willing to stand and fight and defend their posts ... indicates that there's a problem with morale, there's a problem in terms of commitment," Obama said. "Ultimately, that's rooted in the political problems that have plagued the country for a very long time."
Western officials have long complained that Maliki has done little to heal sectarian rifts that have left many of Iraq's minority Sunnis, cut out of power since Saddam Hussein's demise, aggrieved and vengeful - a mood exploited by ISIL.
A U.S. counterterrorism official questioned whether ISIL had the capacity to turn "tactical victories in Iraq into strategic gains," noting that with just a few thousand fighters it was relying on Sunni nationalist groups that might not back it in the long run.
"There are still plenty of things that could go wrong for a group that typically has done well on its home Sunni turf but, if Syria is any guide, is hardly invincible when confronted in unfriendly territory by capable and motivated fighters," the official said.
The ISIL advance has been joined by former Baathist officers who were loyal to Saddam as well as disaffected armed groups and tribes who want to oust Maliki. Cities and towns that have fallen to the militants so far have been mainly Sunni and the gains have largely been uncontested.
It had long been known that Mosul, a city of two million people, harboured not just ISIL but also the Baathist militant group the Naqshbandi Army, believed to be headed by Ezzat Ibrahim al Douri, a former close aide to Saddam.
After the fall of Saddam to the U.S.-led invasion in 2003, officers from the old Iraqi army who had not been reconciled to the new order collected in the Mosu l area. The city's proximity to the border with Syria allowed Baathists - Saddam's political party - and Islamic radicals freedom of movement.
U.S. AND IRAN INTERESTS COINCIDE
On the advance, a member of the Mujahideen Army, consisting of ex-military officers and more moderate Islamists, said: "We were contacted by ISIL around three days before the attack on Mosul asking us to join them. Speaking honestly we were reluctant to join as we were not satisfied they could do the job and defeat thousands of government troops in Mosul.
"When ISIL entered Mosul and swept out government forces positions in hours ... Only then did we decide to join forces and fight with them as long as we had a sole objective to kick Maliki forces out of Mosul and remove injustice."
The pace of events means that now, an alarmed Shi'ite Islamic Republic of Iran, which in the 1980s fought Saddam for eight years at a time when the Sunni Iraqi leader enjoyed quiet U.S. support, may be willing to cooperate with the "Great Satan" Washington to bolster mutual ally Maliki.
The idea is being discussed internally among the Tehran leadership, a senior Iranian official told Reuters, speaking on condition of anonymity. "We can work with Americans to end the insurgency in the Middle East," the official said, referring to the sudden escalation of conflict in Iraq.
The U.S. State Department said Washington was not discussing Iraq with Tehran.
Thrusting further to the southeast after their seizure of Mosul in the far north and Saddam's hometown of Tikrit, ISIL entered two towns in Diyala province bordering Iran.
Saadiyah and Jalawla had fallen to the Sunni Muslim insurgents after government troops fled their positions.
Iraqi army units subsequently subjected Saadiyah and Jalawla to artillery fire from the nearby town of Muqdadiya. ISIL fighters eventually withdrew from Jalawla and well-organised Kurdish Peshmerga fighters took over. Iraqi army helicopters fired rockets at one of the largest mosques in Tikrit on Friday, according to witnesses. There were no further details available.
"CHANCE TO REPENT"
Giving a hint of their vision of a caliphate, ISIL published sharia rules for the realm they have carved out in northern Iraq, including a ban on drugs, alcohol, cigarettes and an edict on women to wear only all-covering, shapeless clothing.
ISIL militants were reported to have executed soldiers and policemen after their seizure of some towns.
On Friday, ISIL said it was giving soldiers and policemen a "chance to repent ... For those asking who we are, we are the soldiers of Islam and have shouldered the responsibility to restore the glory of the Islamic Caliphate".
Residents near the border with Syria, where ISIL has exploited civil war to seize wide tracts of that country's east, watched militants bulldozing tracks through frontier sand berms.
ISIL has battled rival rebel factions in Syria for months and occasionally taken on President Bashar al-Assad's forces.
ISIL's Syria branch is now bringing in weapons seized in Iraq from retreating government forces, according to Rami Abdulrahman, head of the Syrian Observatory for Human Rights monitoring group. But its fighters appear to have held back in Syria, especially in their eastern stronghold near the Iraqi border, while their Iraqi wing was making rapid military gains.
At Baiji, near Kirkuk, ISIL fighters ringed Iraq's largest refinery, underlining the incipient threat to the oil industry.
Further south, militant forces extended their advance to towns about an hour's drive from Baghdad, where Shi'ite militia were mobilising for what could be a replay of the ethnic and sectarian bloodbath of 2006 and 2007. Trucks carrying Shi'ite volunteers in uniform rumbled to front lines to defend Baghdad.
SADR HOLDS FIRE
Despite the call to arms from Sistani, influential Shi'ite cleric Moqtada al-Sadr, who led revolts against U.S. forces, has not called on his followers to mobilise. At Friday prayers, his faithful were told to wait for directions in the coming days on how to form "peace regiments" that will defend holy sites.
Maliki's army already lost control of much of the Euphrates valley west of the capital to ISIL last year. With the evaporation of the army in the Tigris valley to the north, the government could be left with just Baghdad and areas south - home to the Shi'ite majority in Iraq's 32 million population.
ISIL has set up military councils to run the towns they captured. "'Our final destination will be Baghdad, the decisive battle will be there' - that's what their leader kept repeating," said a regional tribal figure. (Additional reporting by Oliver Holmes in Beirut, Ziad al-Sinjary in Mosul Isabel Coles in Arbil, Steve Holland and Mark Hosenball in Washington; Writing by Peter Millership and David Alexander; Editing by Mark Heinrich and David Storey)