Al-Dulaimi said their representatives would not attend cabinet meetings until proceedings against Hashemi in connection with a murder investigation were halted.
An arrest warrant has been issued against Hashemi, who is accused of involvement in an attack on Mithal Alussi, a Sunni independent MP, in February 2005.
Alussi escaped the attack in Baghdad but his two sons were killed. Hashemi has gone into hiding after the allegations were levelled him.
"These are fabricated accusations. We want to form a neutral committee to find out the details of this case"
Alaa Meki, a senior member of the moderate Iraqi Islamic Party
"These are fabricated accusations. We want to form a neutral committee to find out the details of this case," Alaa Meki, a senior member of the moderate Iraqi Islamic Party, which belongs to the Accordance Front, said.
An MP from the Shia United Iraqi Alliance insisted that Hashemi's case was a judicial matter, rather than a campaign against the Accordance Front.
"They are proclaiming the minister's innocence in spite of all the evidence that has been presented in the case," Askari said.
The decision of the Accordance Front to suspend participation in Iraq’s cabinet and parliament will disappoint the US.
Washington has sought the passage of major laws aimed at drawing Sunni Arabs more firmly into the political process, but none of the drafts have reached parliament.
The laws deal with the sharing of revenues from Iraq's huge oil reserves, holding provincial elections and amending a ban on former members of Saddam Hussein's Baath party serving in the government and military.