The al-Mahdi Army is led by Muqtada al-Sadr, a Shia religious leader opposed to the US military presence in Iraq.
 
Fresh clashes
 
The attacks on the Green Zone came after at least 10 people were killed in clashes between Shia fighters and US and Iraqi forces in Sadr City.
 
At least 44 people were hurt in the violence, which broke out at 6:00 pm (1500 GMT) on Saturday and continued past dawn on Sunday, officials from the defence and interior ministries said.
 
A medical official said that eight people, including a woman, died in night-time clashes.
 
The US military said that two fighters were killed between 8.30 am and 10.50 am on Sunday in separate attacks on US forces in Sadr City.
 
'Stop bloodshed'
 
The fighting in Sadr City came after al-Sadr said that fighting between his al-Mahdi Army militia and Iraqi security forces should end.

He called on Friday for "my brothers in the army, police and Jaish al-Mahdi [al-Mahdi Army] to stop the bloodshed".

Al-Sadr had warned on April 19 that an all-out war between government forces and the al-Mahdi Army could break out unless attacks on his fighters were stopped.

The violence in Sadr City is the latest in a crackdown against Shia fighters by forces from the Shia-led Iraqi government.

Hundreds of people are thought to have died in the operation by government forces since it was launched in the southern city of Basra and Sadr City in late March.

Sunni call

Also on Saturday, Iraq's Sunni vice-president said that the return of his political bloc to the Shia-led cabinet was a priority.

Tariq al-Hashemi, who is a member of the National Accordance Front, said the government needs to reconcile quickly to "save Iraq".

The National Accordance Front has boycotted the Iraqi government for nearly nine months.

Al-Hashemi has in the past accused Nuri al-Maliki, Iraq's Shia prime minister, of sectarian favouritism.

Al-Maliki has denied the accusation, saying that al-Hashemi has sought to undermine key legislation.