"This suspension is for one week. "We are waiting for a positive response from the other parties, to see if they will deal with our demands seriously," said Abdullah.
Hoda Abdel-Hamid, Al Jazeera's Iraq correspondant, said: "The bloc's main point on contention is the release of prisoners that have been detained with no charges.
"But also that Iraqi security forces have been targetting more Sunni areas and fighters than Shia forces.
"These demands could also mean the disbanding of the Iraqi government security forces, since they have been accused of being infiltrated by these militas."
The Front's Sunni ministers boycotted al-Maliki's coalition government after an arrest warrant was issued in June against Asaad Kamal al-Hashemi, the culture minister.
The minister is accused of plotting to kill Mithal Alussi, a Sunni MP, in an ambush in February 2005.
Alussi escaped the assault but his two sons were killed.
The Front had originally ended a month-long parliamentary boycott on July 19, and saw one of its leading members, Mahmud Mashhadani, reinstated as speaker of the Iraqi National Assembly.
The return of the Sunni parliamentary bloc was seen as a boost to the as it struggles to pass key legislation aimed at promoting national unity.
Abdel-Hamid said: "These people are described as the moderate Sunnis - those that have decided to take a chance and participate in the Shia-led government.
"The worrying problem is if the Sunni bloc pulls out [of the government] permanently.
"Al-Maliki can still pass laws and go about his business but it will damage any attempt to bring about national reconciliation."