(Adds corpses found in Muqdadiya, north of Baghdad)
BAGHDAD, July 17 (Reuters) - A suicide bombing claimed by the Islamic State militant group killed three people on Thursday in the centre of Baghdad and a second bomb outside the Iraqi capital killed six people, police and medics said.
The bomb in central Baghdad, claimed by the al Qaeda offshoot, exploded near the Shi'ite mosque of Abdullah bin Rawah in the main wholesale market of Shorja, the sources said.
The Islamic State said on an affiliated Twitter feed that a man it called Abu Bakr al-Australi (the Australian) had detonated explosives in a vest he was wearing near the mosque.
The other suicide bomber detonated an explosive-rigged car at a checkpoint on the northern exit from Baghdad, killing six people and wounding 18, most of them policemen, sources said.
The army and allied Shi'ite militia forces are trying to push back Sunni insurgents, who swept through northern Iraq last month to within 70 km (45 miles) of Baghdad.
An army offensive to retake the northern city of Tikrit on Tuesday was repulsed by the insurgents, who forced troops to pull back south of the city on the banks of the Tigris.
The fighting has exacerbated a political crisis in Baghdad, where Shi'ite caretaker Prime Minister Nuri al-Maliki is trying to form a government in the face of opposition from Sunnis, Kurds and some Shi'ites, three months after Iraq held a parliamentary election.
Iraq's Shi'ite clergy as well as Western powers have pressed politicians to overcome their deadlock and agree a new unity government to help tackle the insurgency and prevent Iraq from splitting down ethnic and sectarian lines.
To the north of Baghdad, militants attacked the Turkuman town of Amirli overnight on Wednesday and on Thursday morning, striking from three directions. Nine insurgents and one soldier were killed in the fighting, Amirli mayor Talib Mohammed said.
Police in Muqdadiya, a town 80 km (50 miles) northeast of the capital, said they found 10 corpses with execution-style bullet wounds in their heads and chests on a street late on Thursday. A local morgue source confirmed the deaths.
Residents in the town had on Monday found 12 corpses with execution-style bullet wounds after fighting between Islamic State fighters and the Naqshbandi Army, a group led by supporters of Sunni former dictator Saddam Hussein's Baath Party. (Reporting by Raheem Salman; Editing by Louise Ireland)