(Adds Sistani comments)
* Troops massing around Samarra, officials see push back
* Obama offers 300 military advisers, presses political solution
* Senior Shi'ite cleric urges new government, calls for unity
* Prime Minister Maliki criticised in Washington
* Fighting continued around Baiji refinery
* New fighting in Diyala province
* UN warns against air strikes
By Isra' al-Rubei'i
BAGHDAD, June 20 (Reuters) - Iraqi forces were massing north of Baghdad on Friday, aiming to strike back at Sunni Islamists whose drive toward the capital prompted the United States to send military advisers to stiffen government resistance.
Iraq's senior Shi'ite religious cleric issued a call for unity, saying Shi'ites and Sunnis should rally behind the authorities to prevent the Sunni militant Islamic State of Iraq and the Levant from destroying the country.
Already, ISIL has started to enact its puritanical vision of Islam in Mosul, which it captured 10 days ago as it swept across northern Iraq. Mosul residents said ISIL members had destroyed symbols of Iraq's rich heritage, razing statues of cultural icons and the tomb of a Mediaeval philosopher.
President Barack Obama offered on Thursday up to 300 American special forces advisers to help the Iraqi government recapture territory across northern and western Iraq that ISIL and other Sunni armed groups have seized.
But he held off granting a request for air strikes to protect the government and renewed a call for Iraq's long-serving Shi'ite prime minister Nuri al-Maliki to do more to overcome sectarian divisions that have fuelled resentment among the Sunni minority.
In office since 2006, Maliki has disappointed Washington by alienating Sunnis. Obama has called for a more inclusive government in Baghdad, although he has stopped short of saying Maliki should be replaced. There has been speculation Maliki may also have lost the confidence of allies in Iran.
Tehran and Washington have both spoken of cooperating with each other after decades of mutual hostility to prevent anti-Western, anti-Shi'ite zealots controlling swathes of Iraq.
In the area around Samarra, on the main highway 100 km (60 miles) north of Baghdad, which has become a frontline of the battle with the ISIL, the provincial governor, a rare Sunni supporter of Maliki, told cheering troops they would now force ISIL and its allies back.
A source close to Maliki told Reuters that the government planned to hit back now that it had halted the advance which saw ISIL seize the main northern city of Mosul, capital of Nineveh province, 10 days ago and sweep down along the Sunni-populated Tigris valley toward Baghdad as the U.S.-trained army crumbled.
Governor Abdullah al-Jibouri, whose provincial capital Tikrit was overrun last week, was shown on television on Friday telling soldiers in Ishaqi, just south of Samarra: "Today we are coming in the direction of Tikrit, Sharqat and Nineveh.
"These troops will not stop," he added, saying government forces around Samarra numbered more than 50,000.
This week, the militants' lightning pace has slowed in the area north of the capital, home to Sunnis but also to Shi'ites fearful of ISIL, which views them as heretics to be wiped out. Samarra has a major Shi'ite shrine.
The participation of Shi'ite militias and tens of thousands of new Shi'ite army volunteers has allowed the Iraqi military to rebound after mass desertions by soldiers last week allowed ISIL to carve out territory where it aims to found an Islamic caliphate straddling the Iraqi-Syrian border.
"The strategy has been for the last few days to have a new defence line to stop the advance of ISIL," a close ally of Maliki told Reuters. "We succeeded in blunting the advance and now are trying to get back areas unnecessarily lost."
Fighting continues in pockets. Government forces appeared to be still holding out in the sprawling Baiji oil refinery, the country's largest, 100 km north of Samarra, residents said.
At Duluiya, between Samarra and Baghdad, residents said a helicopter strafed and rocketed a number of houses in the early morning, killing a woman. Police said they had been told by the military that the pilot had been given the wrong coordinates.
Fighting flared in Muqdadiya in northeastern Diyala province, where security forces attacked a swathe of orchards dominated by Sunni militants, and 1,000 civilians fled north for safety, according to a security source. State television accused the extremists of displacing the Sunnis as a propaganda tool to embarrass the state.
CALL FOR UNITY
Grand Ayatollah Ali al-Sistani, the most respected Shi'ite cleric in Iraq, pleaded for stability and for Iraqis to stop their country from falling into the abyss.
In a speech read by an aide, the reclusive octogenarian, who rarely leaves home, urged Sunnis and Shiites to stand together against ISIL and called on the country's politicians to soon convene the newly-elected parliament so the process of forming the government could begin.
Many Iraqis fear the political class will postpone the government formation as long as possible to take advantage of the current chaos. Sistani reemphasised a call made a week ago for civilians to volunteer and fight ISIL through the Iraqi security forces.
He described his message as a call to arms for all Iraqis, not just his sect. His appeal was widely seen as giving a boost to a government and armed forces that had been deeply shaken in its war with Sunni armed groups, dominated by ISIL.
"If fighting and dislodging them is not done today, all will feel sorry tomorrow," Sistani said.
In Mosul, where ISIL stunned Iraq by seizing the north's biggest city, the militant group, which had sought alliances with other armed Sunni factions, has started to impose its strict interpretation of Islam.
Witnesses, speaking on condition of anonymity, said ISIL has destroyed a statue of Othman al-Mousuli, a 19th Century Iraqi musician and composer, and the statue of Abu Tammam, a Mediaeval Arab poet.
The group has also desecrated the tomb of Ibn al-Athir, an Arab philosopher who travelled with the army of warrior sultan Salahuddin in the 12th century, they said. Under ISIL's interpretation of Islam, tomb shrines are a form of idolatry.
During the U.S. occupation from 2003-2011, ISIL, then known as the Iraq branch of al Qaeda, alienated many Sunnis with its strict and violent interpretation of Islam, leading tribesmen to join forces with U.S. troops and the Baghdad government. But this time around, Sunni tribes are so angry with Maliki that many have joined the revolt alongside ISIL.
Obama has ruled out sending ground troops back to Iraq, two and half years after he withdrew them.
Announcing the despatch of advisers, the president said he was prepared to take "targeted" military action later if deemed necessary, thus delaying but still keeping open the prospect of air strikes to fend off the insurgency.
Obama also delivered a stern message to Maliki on the need to take urgent steps to heal Iraq's sectarian rift, something U.S. officials say the Shi'ite leader has failed to do and which ISIL has exploited to win broader support among the Sunnis.
"We do not have the ability to simply solve this problem by sending in tens of thousands of troops and committing the kinds of blood and treasure that has already been expended in Iraq," Obama told reporters. "Ultimately, this is something that is going to have to be solved by the Iraqis."
The contingent of up to 300 military advisers will be made up of special forces and will staff joint operations centres for intelligence sharing and planning, U.S. officials said.
Leading U.S. lawmakers have called for Maliki to step down, and Obama aides have also made clear their frustration with him.
While Obama did not join calls for Maliki to go, saying "it's not our job to choose Iraq's leaders", he avoided any expression of confidence in the embattled Iraqi prime minister.
U.N. Secretary-General Ban Ki-moon told the Security Council Friday air strikes "might have little lasting effect or even be counter-productive if there is no movement towards inclusive government." (Additional reporting by Raheem Salman, Ned Parker and Oliver Holmes in Baghdad, Ghazwan Hassan in Tikrit and Patricia Zengerle, Susan Heavey, Roberta Rampton, Mark Felsenthal and Jeff Mason in Washington; Writing by Ned Parker and Alastair Macdonald; Editing by Peter Graff)