* Government aims to regain north Iraq from jihadi militants
* Awja village just south of insurgent-held city of Tikrit
* Sistani says lack of new government "regrettable failure" (Adds fighting in town of Hawija near Kirkuk)
By Isra'a al-Rubei'i and Maggie Fick
BAGHDAD, July 4 (Reuters) - The Iraqi army retook Saddam Hussein's home village overnight, a symbolic victory in its struggle to seize back swathes of the country from Sunni insurgents.
Backed by helicopter gunships and helped by Shi'ite Muslim volunteers, the army recaptured the village of Awja in an hour-long battle on Thursday night, according to state media, police and local inhabitants.
Awja lies 8 km (5 miles) south of Tikrit, a city that remains in rebel hands since Islamic State, formerly the Islamic State in Iraq and the Levant (ISIL), launched a lightning assault across northern Iraq last month.
The offensive to retake Tikrit began on June 28, but the army has still failed to retake the city which fell after the police and army imploded last month in the face of the militant onslaught that also captured Mosul and other major Sunni areas.
The military spokesman of embattled Shi'ite Prime Minister Nuri al-Maliki said Awja had been "totally cleansed" and 30 militants killed, according to state television. A police source told Reuters three insurgents had been killed.
The birthplace of Saddam, Awja benefited hugely from the largesse of the Sunni dictator before his ousting by the U.S. invasion of 2003 and locals remained fiercely loyal to the man who would select his relatives from the area for top posts.
Spokesman Qassim Atta said security forces had seized control of several government buildings, including a water treatment plant, but security sources and residents said militants were still holding Iraqi forces from entering Tikrit.
The army said it now held the 50-km (30-mile) stretch of highway running north from the city of Samarra - which is 100 km (60 miles) north of Baghdad - to Awja.
But the mainly Sunni communities along this corridor remain hostile towards government forces and army convoys continue to come under guerrilla attack.
Military officials in the United States, which has deployed advisers to Iraq, believe the Iraqi army will be able to defend Baghdad but struggle to recapture lost territory, mainly because of logistical weaknesses.
Government forces could benefit if cracks in the loose alliance of insurgents in Sunni majority areas widens.
In the town of Hawija, site of infighting last month between Islamist fighters and Sunni militia forces, members of local Sunni tribes told Reuters that community members had organised to fight against the militants in control of the town.
Members of the Al-Obaidi tribe were angered over the militants' seizure of homes of local sheikhs and officials and had formed an armed group that killed five insurgents on patrol in the town on Friday, residents said.
The onslaught by Islamic State, an al Qaeda splinter group that has declared a medieval-style Islamic caliphate erasing the borders of Iraq and Syria, and threatened to march on Baghdad, has left the Shi'ite-led government in disarray.
Parliament was unable this week to pick a new government to unite the ethnically divided country, something the most senior Shi'ite cleric on Friday called a "regrettable failure".
In a sermon delivered by his aide, Sistani Grand Ayatollah Ali al-Sistani called on politicians to avoid "mistakes of the past that have grave consequences for the future of the Iraqis."
Sistani reiterated his call for the government to have "broad national acceptance", a formulation many officials interpret as a call for Maliki - blamed by Sunnis for marginalising them and worsening ethnic tensions - to go.
In the governing system set up after Saddam's fall, the prime minister has traditionally been Shi'ite, the speaker of parliament a Sunni and the largely ceremonial president a Kurd.
None of the blocs has settled on a nominee.
On June 13, Sistani called for Iraqis to take up arms against the insurgency - an unusually assertive declaration for the 83-year-old cleric, who favours a behind-the-scenes role.
In the Friday sermon, he reiterated volunteer fighters should be organised through an official framework.
The president of Iraq's autonomous Kurdish region asked its parliament on Thursday to plan a referendum on independence. Although they share Baghdad's determination to face down the Islamist insurgency, many Kurds see the crisis as a golden opportunity to create their own state. (Additional reporting by Raheem Salman and Alexander Dziadosz in Baghdad and Isabel Coles in Arbil; Writing by Maggie Fick; Editing by Robin Pomeroy)