Iraqi Prime Minister Ibrahim Jaafari has said he is confident that the country's politicians will reach an agreement on a new constitution.
The Iraqi media has been promoting the constitution
On Monday, politicians submitted a draft document to parliament, but MPs did not vote on it because several key issues were still unresolved.
Iraqi MPs gave negotiators three more days to reach agreement on the draft.
On Tuesday, politicians again resumed negotiations aimed at resolving differences related to federalism.
Sunni Arab representatives fear that further provincial devolution could lead to the break-up of the country.
We have made an important stride
Kurdish officials were also against imposing a text without Sunni approval.
The original deadline was last week, but it was shifted to midnight on Monday (2000 GMT) when no agreement was reached.
Mr Jaafari said that 151 of 153 articles of the constitution had been agreed. He insisted the issue of federalism had been settled.
"We have made an important stride," he said.
Distribution of Iraq's oil wealth has been a key stumbling block to a deal
Earlier, the head of the committee responsible for drafting the constitution, Humam Hammoudi, said he did not think the three days political leaders had given themselves to agree a deal would be enough.
Mr Hammoudi, said the leaders might have to find a way of postponing discussion of some of the issues.
In Washington, the White House welcomed "another step forward" in the work on the constitution.
US officials have been pressuring Iraqi politicians to push through an agreement on the constitution, arguing that a delay risks playing into the hands of the insurgents.
Sunnis have expressed concerns that allowing for federalism may lead to the creation of an autonomous Shia area in southern Iraq - like the Kurdish north but under Iran's influence.
The Sunnis fear greater autonomy for the Kurdish north and Shia south could compromise their share of revenues from those oil-rich regions.
Shia and Kurdish political groups have enough of a majority in parliament to push through a draft constitution without the support of Sunni members of parliament, but correspondents say this would be a politically damaging move.
Iraqi parliament speaker Hajim Hassani opened the a late-night session on Monday saying a draft had been received but outstanding issues remained.
- federalism, and the way to form [federal] regions
- the terminology used in eradicating the influence of the former Baath regime - whether to use the term Baath party or Saddam's Baath
- structuring of authority between the presidency, parliament and the government.
There was strong interest in reaching unanimity on the draft "so that the constitution pleases everyone", Mr Hassani said.