Iraqi negotiators have been given three more days to reach agreement on the draft of a new constitution.
The Iraqi media has been promoting the constitution
MPs met for a brief session minutes before the 2000 GMT deadline to receive the draft expired, but did not vote.
The session came after a day of drama during which Shia negotiators said a text had been agreed with the Kurds.
But Sunni Arabs protested - saying the document may lead to Iraq being split up. Kurds 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.
In Washington, the White House welcomed "another step forward" in the work on the constitution.
"The progress made over the past week has been impressive," said a statement, adding that democracy was "difficult and often slow, but leads to durable agreements".
The Iraqi Foreign Minister, Hoshyar Zebari, told the BBC that it was important not to force agreement on Sunnis, and he played down the scale of remaining differences.
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.
US officials say a delay risks playing into the hands of the insurgents, who killed 10 people in Baghdad on Monday.
Eight policemen were among those killed as their mini-van was riddled with bullets north of the capital.
Iraqi parliament speaker Hajim Hassani opened the session 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.
Parliament met after much confusion over whether agreement had been reached - and whether Shias and Kurds would try to impose the deal to parliament.
"Thank God we have finished all the details related to the agreement," Shia negotiator Jawad Maliki announced hours before the midnight deadline.
Sunni negotiator Saleh Mutlaq told the BBC that violence could ensue if there was an attempt to impose a constitution, which would be defeated in a referendum.
Iraq has a wealth of oil, but the infrastructure needs improving
Mr Mutlaq complained that Shias and Kurds had met all week without their Sunni counterparts on the drafting committee and the Sunnis had been given a text a few hours before the deadline on Monday.
He said their amendment to exclude federalisation had been taken out of the draft text, which was worrying for the Sunnis.
"There will be a big federal state in the south connected to Iran" and under Tehran's influence, he told the Newshour programme.
"With time these regions will separate from each other," Mr Mutlaq said.
One prominent Kurdish negotiator, Mahmoud Othman, said earlier the Shia insistence on submitting the draft had created a lot of bad feeling.
A draft constitution is due to be put to a referendum in October.
If it is approved, fresh elections would follow to elect a fully-mandated parliament under its terms, probably in December.