* Government aims to regain north Iraq from jihadi militants
* Awja village just south of insurgent-held city of Tikrit
* US: Iraq army will struggle to regain territory by itself
By Isra al-Rubei'i and Maggie Fick
BAGHDAD, July 4 (Reuters) - The Iraqi army drove Sunni insurgents out of late dictator Saddam Hussein's home village, state media and police said, part of a campaign to retake wide areas of northern and western Iraq overrun by the rebels.
The al Qaeda splinter group leading the insurgency has declared a medieval-style Islamic caliphate erasing the borders of Iraq and Syria, and threatened to march on the Iraqi capital Baghdad to topple the Shi'ite-led central government.
Pursuing a counter-offensive, government forces along with Shi'ite Muslim volunteers backed by helicopter gunships recaptured the village of Awja on Thursday night, according to state media, police and local inhabitants.
They said three insurgents were killed in an hour-long battle, and the main body of militant forces had fled south along the eastern bank of the Tigris River across from Awja.
State television quoted the prime minister's military spokesman, Qassim Atta, as saying that Awja had been "totally cleansed" and 30 militants had been killed. No casualty figures could be independently verified.
The army said it now held the 50 km (30-mile) stretch of main 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 remained hostile towards government forces and their convoys were coming under guerrilla attack, while the city of Tikrit a few km north of Awja remained in the grip of insurgents.
Tikrit fell early in the lightning offensive last month that gave jihadi militants led by the Islamic State, formerly known as the Islamic State in Iraq and the Levant (ISIL), control of most majority Sunni regions north of Baghdad.
During his decades-long rule until his fall to a U.S.-led invasion in 2003, Saddam Hussein surrounded himself with relatives from Awja and Tikrit, creating a praetorian circle of aides from the Sunni Arab Albu Nasir tribe.
Among the fighters Iraqi forces repelled from Awja were members of the Naqshbandi Army, made up of former army officers as well as loyalists of Hussein's old Baathist party.
Though Islamists and old Baathists have banded together to fight their common foe - the government of Shi'ite Prime Minister Nuri al-Maliki - cracks are showing in their loose bloc as many Baath party veterans do not hold jihadist views.
In the town of Hawija near the northern city of Kirkuk, 15 people were killed when fighting broke out a fortnight ago between the Islamic State and members of the Naqshbandi Army.
BAGHDAD WILL STRUGGLE TO REGAIN LOST TERRITORY -U.S.
Top U.S. defence officials, who have deployed advisers to Iraq to assess the state of its military, believe it will be able to defend Baghdad but struggle to recapture lost territory, mainly because of logistical weaknesses.
"If you're asking me will the Iraqis at some point be able to go back on the offensive to recapture the part of Iraq that they've lost, I think that's a really broad campaign quality question," General Martin Dempsey, chairman of the U.S. Joint Chiefs of Staff, told reporters in Washington.
"Probably not by themselves."
Dempsey said "the future is pretty bleak" for Iraqis unless they can bridge sectarian differences within their Shi'ite-dominated government. The absence of an inclusive government giving all of Iraq's main communities a say in power, he said, helped explain ISIL's almost unopposed onslaught last month.
The president of Iraq's autonomous Kurdish region asked its parliament on Thursday to plan a referendum on Kurdish independence, signalling his impatience with Maliki's embattled government.
Massoud Barzani's call came days after Kurds and Sunnis walked out of the newly elected Iraqi parliament's first session in Baghdad, complaining that the majority Shi'ites had failed to nominate a new prime minister.
Iraq's 5 million Kurds, who have governed themselves in relative peace since the 1990s, have expanded their territory by as much as 40 percent in recent weeks as the sectarian insurgency has threatened to split the country.
Many Kurds have long wanted to declare independence and now sense a golden opportunity, with Baghdad weak and Sunni armed groups in control of northern cities such as Mosul and Tikrit.
Growing alarm about the wider regional security threat posed by ISIL and pressure from the United States, United Nations, Iran and Iraq's own Shi'ite clerics have done little to end paralysing splits between Iraq's key ethnic and sectarian blocs.
(Reporting by Isra al-Rubei'i; Writing by Maggie Fick; Editing by Mark Heinrich)