* PM-designate says new government to agree "clear vision"
* Abadi faces tough task overcoming sectarian divisions
* Suicide bomber kills at least nine in Baghdad
* Car bomb attacks also hit Karbala, Hilla on Monday
By Ahmed Rasheed
BAGHDAD, Aug 25 (Reuters) - Iraq's Prime Minister-designate Haider al-Abadi said on Monday he was optimistic about forming a new government soon with a "clear vision", but fresh bomb attacks in Baghdad and other cities underlined the country's deepening sectarian conflict.
Abadi is tasked with forming a power-sharing administration that can ease tensions and counter Islamic State militants who pose the biggest security threat to Iraq since a U.S.-led invasion toppled Saddam Hussein in 2003.
"The talks to form the government were positive and constructive. I hope in the next two coming days to agree on a clear vision of a unified programme for the government," he said.
Shortly after Abadi spoke, a suicide bomb attack in a Shi'ite mosque in Baghdad killed at least nine people and wounded 21, police and medical sources said.
The attacker detonated his suicide bomb vest inside the mosque in the New Baghdad district of the capital at prayer time, police said.
Two car bombs were also detonated in the Shi'ite holy city of Karbala on Monday, killing four people and wounding 17, police and medical sources said. An additional two car bombs targeted the city of Hilla, south of Baghdad, but there were no fatalities or injuries, police sources said.
The Islamic State claimed responsibility for four car bombs in northern Iraq on Saturday, three of them in the city of Kirkuk, where Kurdish fighters have flocked since Iraqi army units quit their posts in June, and one in Arbil, capital of the autonomous Kurdish region.
The militant group said the attacks were in response to Kurdish forces joining the U.S. military to attack them.
Abadi, keen to reassert Baghdad's authority over his fraying nation, emphasized in his comments on Monday he would not tolerate armed groups operating outside government control.
"We will not allow the formation of armed groups outside the control of the state," he said.
Abadi added that arms reaching the Kurdish peshmerga forces battling Islamic State militants in the north had passed through the central government.
Many ordinary Iraqis have expressed concern about the unchecked growth of violent militia groups in recent weeks, some of whom have been accused of targeting civilians.
In June, Ayatollah Ali Sistani, Iraq's most senior Shi'ite cleric, urged Iraqis to defend the country against the onslaught of Islamic State militants. As a result thousands of volunteers, many of them Shi'ites, joined militia groups which are now only nominally under the control of the Baghdad government.
Shi'ite militants are suspected of carrying out an attack on a Sunni mosque in Diyala province north of Baghdad last Friday that killed 68 and wounded dozens.
The central government has issued arrest warrants for four local tribesmen suspected of carrying out the attack after an investigation, Abadi said on Monday.
Foreign Minister Mohammad Javad Zarif of Iran, a key ally of the Shi'ite-led Baghdad government, visited the holy city of Najaf for talks with Sistani and other senior Shi'ite clerics, local officials said.
Sistani played a key role in helping to resolve Iraq's recent political crisis by implicitly urging former prime minister Nouri al Maliki to step down. Maliki, a Shi'ite, was widely accused of exacerbating Iraq's sectarian divisions by excluding Sunni Muslims from positions of influence.
Iran's Zarif also met a handful of Sunni political leaders in Baghdad on Monday evening to discuss the formation of the new government, the Islamic Republic News Agency (IRNA) reported. (Additional reporting by Kareem Raheem; Writing by Babak Dehghanpisheh; Editing by Gareth Jones) ((firstname.lastname@example.org;)(00-964-7801-718-985) )