* Parliament's first session collapsed without agreement
* Baghdad residents express frustration at political squabbles
* Air strike in Shirqat kills 11 - witnesses and medics
* Islamic State militants have declared "caliphate" (Adds Maliki quotes, fighting in southern city of Karbala)
By Ahmed Rasheed and Alexander Dziadosz
BAGHDAD, July 2 (Reuters) - Iraqi Prime Minister Nuri al-Maliki, who is fighting for his political life as a Sunni insurgency fractures the country, said on Wednesday he hoped parliament could form a new government in its next session after the first collapsed in discord.
Baghdad can ill afford a long delay. Large swathes of the north and west have fallen under the control of an al Qaeda splinter group that has declared it is setting up a "caliphate" and has vowed to march on the capital.
Yet the mounting concern and pressure from the United States, Iran, the United Nations and Iraq's own Shi'ite clerics have done little to end the paralysing divisions between Iraq's main ethnic and sectarian blocs.
Sunnis and Kurds walked out of parliament's first session on Tuesday, complaining that Shi'ites had failed to nominate a prime minister; they see Maliki as the main obstacle to resolving the crisis and hope he will step aside.
Under the system put in place after the United States toppled Saddam Hussein in 2003, the premiership is traditionally given to a Shi'ite, while the speaker of the house has been a Sunni and the president, a largely ceremonial role, has been a Kurd.
In his weekly televised address, Maliki said he hoped parliament could next Tuesday get past its "state of weakness".
"God willing, in the next session we will overcome it with cooperation and agreement and openness," he said. "There is no security without complete political stability."
But it is far from clear when leaders in Baghdad might reach a consensus. All the main ethnic blocs are beset by internal divisions, and none has yet decided who to put forward for its designated position. Sunnis and Kurds say they want Shi'ites to choose a premier before they announce their nominees, while the Shi'ites say the Sunnis should first name the speaker.
"Each bloc has its own problems now," said Muhannad Hussam, a politician and aide to leading Sunni lawmaker Saleh al-Mutlaq.
If the Shi'ite bloc failed to replace Maliki, he said, there was a risk Sunni lawmakers would abandon the political process altogether. "There would be no more Iraq," he said.
NEED TO BE PATIENT
Longtime Maliki ally Sami Askari said forming a government could take until the end of Ramadan, the Muslim fasting month. But he played down the risk of the state collapsing, saying Maliki's caretaker government would continue to function.
"The reality is that we need to be patient," Askari said. "We will have a government in the end -- but not soon."
Residents of Baghdad were increasingly frustrated with the familiar sight of officials squabbling while the country burns.
"I'm so angry with all these politicians," said Dhamee Sattar Shafiq, a university statistics professor, shopping in a mixed neighbourhood of Sunnis and Shi'ites.
"This country is headed for disaster and these men are just working for their own causes."
Down the road, Najaa Hassan, a 54-year-old carpenter, was similarly irritated. "Democracy has brought us many problems that we really don't need," he said.
Outside the capital, fighting flared again. Medical sources and witnesses said at least 11 people, including women and children, had been killed when Iraqi helicopters attacked Shirqat, 300 km (190 miles) north of Baghdad.
Witnesses said the helicopters were targeting a municipal building where militants were sheltering, and that the air strike also hit three nearby houses.
"We have received 11 bodies and 18 wounded from the helicopters' bombardment. Some children are in critical condition," said Hamid al-Jumaili, a doctor in Shirqat's hospital.
The prime minister's military spokesman, Lieutenant General Qassim Atta, made no specific mention of the incident but listed Shirqat as one of several locations where the air force had been active during the past 24 hours.
The government faces a formidable foe in the Islamic State, which shortened its name from the Islamic State in Iraq and the Levant this week and named its leader "caliph", the historical title of successors of the Prophet Mohammad who ruled the Muslim world.
In his first comments since that declaration, the group's leader Abu Bakr al-Baghdadi on Tuesday called on Muslims across the world to take up arms and flock to the "caliphate", which spans territory that has fallen out of governmental control in Syria and Iraq.
The Islamic State has been working with an amalgam of other Sunni groups including Islamist militias, tribal fighters and former army officers and loyalists of Saddam Hussein, many of whom do not share its rigid ideology but are united by a sense of persecution under Maliki's Shi'ite-led government.
Maliki on Wednesday offered an amnesty to tribes who had taken up arms against the government, but excluded those who had "killed and shed blood".
The United Nations said on Tuesday more than 2,400 Iraqis had been killed in June alone, making the month by far the deadliest since the height of sectarian warfare during the U.S. "surge" offensive in 2007.
Maliki's government, bolstered by civilian volunteers and Shi'ite militias, has managed to stop the militant advance short of the capital, but has been unable to take back the cities that government forces abandoned. The army failed last week to take back Tikrit, 160 km (100 miles) north of Baghdad.
Even if Maliki steps aside - something that is still far from certain - few in Baghdad expect that will mean a swift resolution to the crisis.
"His departure would not solve the problem, because Sunnis and Shi'ites will stay at odds with each other and the animosity will continue," said Haidar Jumaa Zeboun, a 31-year-old construction worker in the district of Arasat.
Beyond that, there is deep strife within both the Sunni and Shi'ite communities.
Police and army in the Shi'ite shrine city of Karbala on Wednesday attempted to arrest a controversial cleric, Mahmoud al-Sarkhi, prompting hours of clashes with his followers, said local police spokesman Colonel Ahmed Al-Hasnawi. (Reporting by Isra' al-Rubei'i, Ahmed Rasheed, Maggie Fick and Alexander Dziadosz in Baghdad; Writing by Alexander Dziadosz; Editing by Kevin Liffey)