(Adds fighting south of Baghdad)
* Iraqi army heads north to wrest back Saddam's hometown
* Shi'ite, Sunni parties huddle, eyeing Tuesday deadline
* Iraq's most powerful Shi'ite cleric demands new premier
* PM Maliki seen as too divisive to save Iraq as state
* ISIL battles rival Islamists on Syrian side of border
* Militants attack army camp south of Baghdad
By Raheem Salman and Ned Parker
BAGHDAD, June 28 (Reuters) - Iraqi government forces backed by helicopter gunships began an offensive on Saturday to retake the northern city of Tikrit from Sunni Islamist militants while party leaders pursued talks that could end Prime Minister Nouri al-Maliki's divisive rule.
Politicians in Baghdad and world powers warn that unless security forces recover cities lost to the jihadi insurgents in tandem with a rapid formation of a government that can bring Iraq's estranged communities together, the country could rip apart along sectarian lines and menace the wider Middle East.
On the battlefield, Iraqi troops were trying to advance on Tikrit from the direction of Samarra to the south that has become the military's line in the sand against a militant advance southwards towards Baghdad.
Iraqi special forces already have snipers inside Tikrit University who were dropped by air there in a bold operation on Thursday. Helicopter gunships fired at targets in Tikrit on Saturday and ISIL fighters abandoned Tikrit's governorate building, security sources said. More government troops had been air-dropped in a pocket just north of the city.
Iraqi military spokesman Qassim Atta told reporters in Baghdad on Saturday that 29 "terrorists" were killed on Friday in Tikrit and that militant commanders were struggling because "their morale has started to collapse".
However, the militants were showing resilience and enjoyed the backing of some local Sunni tribes, as well as former ruling Baathists from the era of late Sunni dictator Saddam Hussein - whose hometown was Tikrit - alienated from Maliki's government.
In other parts of the country, such as Jurf al-Sakhar, 53 miles (85km) south of Baghdad, militants from ISIL - the Islamic State in Iraq and the Levant - were on the offensive.
Three police sources said at least 60 ISIL fighters had been killed along with more than 15 Iraqi security forces members when the militant group launched a major attack on an army camp just east of Jurf al-Sakhar, firing mortars and RPG rounds.
"The ISIL terrorists fired many mortars at the camp and then started their offensive. They managed to break into the camp but could not hold their positions due to army helicopters cover," a police colonel said.
Since early June, the radical ISIL has overrun most majority Sunni areas in the north and west of Iraq, capturing the biggest northern city Mosul and fanning southwards.
ISIL vows to re-create a medieval-style caliphate erasing borders from the Mediterranean to the Gulf and they deem all Shi'ites to be heretics deserving death. They boast of executing scores of Shi'ite government soldiers captured in Tikrit.
GRAND AYATOLLAH'S POLITICAL INTERVENTION
In a stunning political intervention on Friday that could mean the demise of Maliki's eight-year tenure, powerful Shi'ite cleric Grand Ayatollah Ali Sistani urged political blocs to agree on the next premier, parliament speaker and president before a newly elected legislature meets in Baghdad on Tuesday.
Saudi King Abdullah pledged in talks with U.S. Secretary of State John Kerry to use his influence to encourage Sunni Muslims to join a new, more inclusive Iraqi government to better combat Islamist insurgents, a senior U.S. official said on Saturday.
Abdullah's assurance marked a significant shift from Riyadh's unwillingness to support a new government unless Maliki, a Shi'ite, steps aside, and reflected growing disquiet about the regional repercussions of ISIL's rise.
"The next 72 hours are very important to come up with an agreement ... to push the political process forward," said a lawmaker and former government official from the National Alliance, which groups all Shi'ite Muslim parties.
The lawmaker, who asked for anonymity due to political sensitivities, said he anticipated internal meetings by various parties and a broader session of the National Alliance including Maliki's State of Law list to be held through the weekend. Some Sunni Muslim parties were to convene later on Saturday.
Iraqi Sunnis accuse Maliki of freezing them out of any power and repressing their community, goading armed tribes to support the insurgency led by the fundamentalist group ISIL. The president of Iraq's autonomous Kurdistan region has also said Maliki should bow out.
Sistani's entry into the fray will make it hard for Maliki to stay on as caretaker leader as he has since a parliamentary election in April. That means he must either build a coalition to confirm himself in power for a third term or step aside.
Sistani's message was delivered after a meeting of Shi'ite factions including the State of Law coalition failed to agree on a consensus candidate for prime minister.
Maliki, whose State of Law coalition won the most seats in the April election, was positioning himself for a third term before the ISIL offensive began. His closest allies say he still aims to stay, but senior State of Law figures have said he could be replaced with a less polarising figure.
"It's a card game and State of Law plays a poker game very well," said the official from the premier's alliance. "For the prime minister, it will go down to the wire."
ISLAMISTS BATTLE ISLAMISTS ON BORDER
In Syria, where ISIL controls large swathes of land, other Islamist rebel groups pursued a counter-offensive in the border town of Albu Kamal, challenging ISIL's grip along the Iraqi-Syrian frontier.
ISIL is a more radical offshoot of al Qaeda that has its roots in Iraq and expanded into Syria shortly after the start of the three-year insurgency against President Bashar al-Assad.
U.S. President Barack Obama has ruled out sending ground forces back to Iraq, where they were for eight years after invading to oust Saddam, but has sent up to 300 advisers, mostly special forces, to help the government take on ISIL.
U.S. defense officials said on Friday that the Obama administration was flying armed aircraft over Iraq although these aimed to collect intelligence and ensure the safety of U.S. personnel on the ground rather than attack targets.
Still, General Martin Dempsey, the top U.S. military officer, said additional U.S. options included going after "high-value individuals who are the leadership of ISIL" and working to protect Iraq's "critical infrastructure".
On Saturday, 11 people were injured when an explosion rocked a health ministry building in insurgent-held Mosul, a local health official said. City residents said the blast was caused by a drone strike but this could not be confirmed and a U.S. official dismissed this possibility.
Residents also reported overnight rocket fire into Mosul, whose fall to ISIL on June 10 was the catalyst for a militant sweep southwards in which they also took border crossings with areas of civil war-racked Syria that they already controlled.
STRUGGLE FOR SHARE OF POWER
Under Iraq's governing system put in place after Saddam's overthrow, the prime minister has always been a Shi'ite, the largely ceremonial president a Kurd and the speaker of parliament a Sunni. Negotiations over the positions have often been drawn out: after the last election in 2010 it took nearly 10 months for Maliki to build a coalition to stay in office.
Divvying up the three posts in the four days before parliament meets, as sought by Sistani, would require leaders from each of Iraq's three main ethnic and sectarian groups to commit to the political process and swiftly resolve their most pressing political problems, above all the fate of Maliki.
Allies of Maliki said Sistani's call for a quick decision was not aimed at sidelining the premier but at putting pressure on all political parties not to drag out the process with typical infighting with Iraq facing disintegration. Even so, they acknowledged Sistani was not happy with Maliki's policies.
"It is other groups telling Sistani they cannot accommodate Maliki for a third term. Sistani doesn't want to get involved in who is the next prime minister, but there has to be progress," said one official from Maliki's State of Law list.
The roadmap is far from smooth. Kurds have yet to agree on a candidate for president and the Sunnis, long riven by intense rivalries and shaken by the loss of their cities to militants, are divided among themselves over the speaker's post.
Iraq's million-strong army, trained and outfitted by the United States at a cost of some $25 billion, largely disintegrated in the north in the face of ISIL's offensive.
Thousands of Shi'ite volunteers have responded to an earlier call by Ayatollah Sistani for all Iraqis to rally behind the military to defeat the jihadist threat. (Additional reporting by Dominic Evans in Beirut; Editing by Mark Heinrich and Pravin Char)