US President Barack Obama has said the new power-sharing agreement in Iraq after eight months of deadlock marks another "milestone" for the country.
Speaking at the G20 summit in Seoul, Mr Obama said the new Iraqi government would be "representative, inclusive and reflect the will of the Iraqi people".
On Thursday, incumbent Shia Prime Minister Nouri Maliki was re-appointed.
But the main Sunni-backed bloc walked out of parliament accusing him of going back on part of the power-sharing deal.
Al-Iraqiyya's leader, former Prime Minister Iyad Allawi, said Mr Maliki had agreed to reinstate four Sunni politicians who were banned earlier this year for alleged ties to Saddam Hussein's now disbanded Baath party.
Mr Maliki has a month to persuade Mr Allawi to join his administration.
At a news conference in South Korea on Friday, Mr Obama stressed the need for leaders from all the main blocs to hold posts in a broad-based government, whose leaders treated all Iraqis as equals.
"There are still challenges to overcome but all indications are that the government will be representative, inclusive and reflect the will of the Iraq people who cast their ballots in the last election," he said.
"This agreement marks another milestone in the history of modern Iraq, once again showing Iraqis are showing their determination to unify Iraq and build its future and that those impulses are far stronger than those who want Iraq to descend into sectarian war and terror," he added.
The president also pledged his country's continuing support for Iraq.
"In going forward, we will support the Iraqi people as they strengthen their democracy, resolve political disputes, resettle those displaced by war and build ties of commerce and co-operation with the United States, the region and the world."
The US military, which currently has fewer than 50,000 soldiers in Iraq, is due to withdraw all of its forces from the country by the end of 2011.
The first move by Iraqi politicians on Thursday was to elect Osama al-Nujaifi - a Sunni Arab member of al-Iraqiyya - as speaker of parliament. He was previously governor of Nineveh province.
MPs were then due to vote on reappointing Mr Talabani, the leader of the Patriotic Union of Kurdistan (PUK), as president. But before the vote could be held, about a third of the al-Iraqiyya MPs walked out.
The BBC's Jim Muir in Baghdad says the al-Iraqiyya members had wanted parliament to pass a motion to remove the stigma of Baathism, which had barred four of the coalition's key figures from taking political office.
Although not opposed to Mr Talabani's re-election itself, they had wanted the motion to be passed before the election of the president. However, other parties disagreed.
"The al-Iraqiyya bloc withdraw for the sake of the country," Nada Jabbouri, one of its MPs, told the BBC afterwards. "There will be another four years like the last previous four years, since from the beginning there is no trust."
But despite the walk-out, the parliamentary session continued and the remaining MPs went on to re-elect Mr Talabani.
As had been agreed in the deal reached on Wednesday, Mr Talabani then handed the task of forming a government to the largest coalition, the National Alliance - a merger of Mr Maliki's State of Law coalition and the Iraqi National Alliance of the radical Shia cleric Moqtada Sadr.
Mr Maliki now has a month to put together a cabinet, during which efforts will be made to draw Mr Allawi back into the process.
Under the power-sharing deal - struck late on Wednesday - Mr Allawi will head a new "National Council for Strategic Policies". Al-Iraqiyya will also get the foreign ministry.
Al-Iraqiyya won two more seats than State of Law in March's election, but neither had enough seats to form a majority government. The tide turned for Mr Maliki in early October when the Iraqi National Alliance backed him.
Our correspondent says that many Iraqis are now cautiously hopeful that they are on the road to a stable government which includes all the main factions and could turn the corner to a better future for the whole country.
Last time round, many Sunnis felt marginalised, and that feeling was a driving force behind the insurgency, he adds.