US President George W Bush has praised the "heroic efforts" of Iraqi lawmakers who failed to meet a deadline to agree a new constitution for the country.
Constitution delay is not a disappointment: Iraq's president
On Monday, Iraq's parliament agreed to extend the deadline until 22 August to enable negotiators to try to resolve their disputes.
US Secretary of State Condoleezza Rice said Iraq's political leaders had made considerable progress.
Stumbling blocks include the issue of federalism and the role of religion.
In an upbeat message sent from his Texas ranch, Mr Bush said the politicians would carry on working "to refine the text and build an enduring consensus".
"I applaud the heroic efforts of Iraqi negotiators and appreciate their work to resolve remaining issues through continued negotiation and dialogue," he said in his statement.
"Their efforts are a tribute to democracy and an example that difficult problems can be solved peacefully through debate, negotiation and compromise."
Ms Rice insisted the delay is proof of democracy at work, and a sign of Iraqi politicians' commitment to building a new Iraq.
"I believe they're going to finish this and I've heard expressions from the Iraqis that they believe that they're going to finish it," she said.
The US has put considerable pressure on Iraq to approve a draft constitution by 15 August.
Now it is playing down the failure to meet that deadline, says the BBC's State Department correspondent Jonathan Beale.
The three-quarters majority needed for an extension was reached by Iraq's lawmakers just 20 minutes before the midnight deadline to present the new constitution expired.
"It was no disappointment, because we have done a lot," Iraqi President Jalal Talabani said, adding that the delay would not "shake the confidence" of the Iraqi people.
"It must be carefully drafted to avoid mistakes in the future."
Iraqi Prime Minister Ibrahim al-Jaafari shared the view.
"We should not be hasty regarding the issues and the constitution should not be born crippled," he said after the parliament session, which lasted only 15 minutes.
"We are keen to have an early constitution, but the constitution should be completed in all of its items," he added.
The constitution needs to be approved by the National Assembly before it can go to a nationwide referendum in October.
Kurdish minister Barhem Saleh told al-Arabiya TV that if no agreement could be reached on the constitution, the National Assembly would have to be dissolved and fresh elections held.
The Shia Muslims and Kurds between them have a parliamentary majority which could see the document passed.
But this has raised concerns that the constitution could alienate the Sunni minority further and could create a backlash when the referendum is held.
Before parliament met, Saleh Mutlaq, a Sunni Muslim member of the panel drafting the constitution, said Sunnis would reject the draft if it contained proposals for a federal Iraq.
Kurdish and Shia members have reportedly dropped demands that the country should be called federal or Islamic, and agreed that the official name should be the Republic of Iraq.
But any devolution of power, beyond the existing autonomy enjoyed by Kurds, remains contentious.