The Shia and Kurds, with the two biggest blocs in the 275-seat, bartered on Thursday over the make-up of the first government since Iraq elections.
"Talks will continue today between the negotiating Kurdish delegation and representatives of the United Iraqi Alliance (UIA) about the formation of the government," Kurdish negotiator Kamal Fuad told AFP.
The Shia candidate for prime minister, Ibrahim Jafari, said on Wednesday it could take as long as two weeks.
Abbas al-Bayati, a member of the Iraqi transitional National Assembly from the UIA, told Aljazeera on Thursday that the meeting of the parliament had exerted pressure on parties to speed up the negotiations.
"We hope within the next week we will be working on issues related to by-laws, presidential election authority, the cabinet, and administration of the transitional period," he said.
Deal in principle
After their session, the Kurds and the UIA were scheduled to meet outgoing interim Prime Minister Iyad Allawi.
"We hope within the next week we will be working on issues related to bylaws, presidential election authority, the cabinet, and administration of the transitional period"
member of the Iraqi transitional National Assembly
According to al-Bayati, Kurds and Shia had agreed in principle on various issues.
"The two sides have agreed in principle after modifying certain demands and have decided to hold talks with the Iraqi list headed by Allawi and Sunni Arabs to form a national unity government," al-Bayati said.
Government negotiations have deadlocked largely on Kurdish demands for written guarantees on their autonomy in the north, the status of the ethnically divided city of Kirkuk and the Peshmerga militia.
Once a cabinet is appointed, the hard work will begin. The next government will draft a permanent constitution, which is due to go to a referendum in October. A new round of elections will follow in December.
"The transitional period will be very decisive as the constitution is going to be drafted, a constitution that meets the needs of Iraqis to maintain security, offer services and put and end to unemployment," al-Bayati said.