The argument began immediately following the selection of Osama al-Nujaifi, a Sunni Arab, as parliament speaker. At that point, the Iraqiya bloc to which he belongs began complaining that the deal they had signed was not being honoured.
Specifically, Iraqiya had called for three of their top members, barred for their alleged ties to Saddam Hussein's Baath party, to be reinstated before voting for a president.
When their demands were not met, some 60 MPs left the chamber.
"We boycotted the session because we showed good intentions to others, but they stabbed us in the back," Saleh al-Mutlak, one of the trio Iraqiya wanted reinstated, told AFP.
"We will not return without international guarantees," he added, without giving specifics.
The power-sharing deal, clinched after three days of intense talks, stipulated that a Sunni Arab hold the post of speaker, and that Talabani and Maliki retain their posts.
The agreement also established a statutory body to oversee security as a sop to former premier Iyad Allawi, who had held out for months to take the job from Maliki after his Iraqiya bloc narrowly won the most seats in the March 7 polls.
But after Nujaifi was named speaker, Iraqiya lawmakers walked out of the parliamentary chamber. After some confusion, the remaining MPs began voting to re-elect Talabani.
Maliki now has 30 days to form his cabinet.
The next meeting of parliament is now scheduled for Saturday.
Iraqiya has said its participation hinged on four conditions: a bill forming the security body; examination by a committee of cases against political detainees; the codifying of the power-sharing deal; and annulling bans against three Iraqiya members for their alleged ties to Saddam Hussein's Baath party.
It said it "hoped it would not be obliged to change its decision to participate in the political process if these conditions are not met."
The backing of Iraqiya, which won most of its support among the Sunni Arab minority that dominated Saddam's regime and has been the bedrock of the anti-US insurgency since the 2003 invasion, was seen as vital to prevent a resurgence of violence.
Kurdish politician Massud Barzani, who brokered the deal, earlier paid tribute to Iraqiya for concessions that had made it possible, and said he hoped Allawi would now agree to head the new National Council for Strategic Policy (NCSP).
Iraqiya MP Mustafa al-Hiti told AFP that US President Barack Obama had "telephoned Allawi to confirm to him that the NCSP would be a decision-making body and that the law creating it would be voted on before the formation of a new government."
Allawi had repeatedly accused Maliki of monopolising security decisions during his first term.
As long as six months ago, US officials floated the idea of a new counterweight to the power of the premier's office as a way of breaking the deadlock over the premiership.
Barzani, president of the autonomous Kurdish region in northern Iraq, had said he expected Washington to endorse the deal, and later on Thursday a White House statement welcomed it as a "big step forward."
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 fact that this emerging Iraqi government is so inclusive basically means that it is a strong rejection of interference of negative external influences in the region," a senior US administration official said.
"Of course, I'm speaking specifically about Iran's attempts to engineer an Iraqi government that was based on a unified sectarian Shia list that would have been a narrow government and not representative of the government of Iraq," he said.
During the coalition talks, Allawi had accused Iran of putting unwarranted pressure on Iraqi leaders to keep the incumbent in office, while Maliki in turn accused the ex-premier of pandering to Sunni Arab states, notably Saudi Arabia.
"I cannot deny there has been regional and international pressure. Often it took the form of conversations and suggestions, but sometimes it amounted to pressure," Barzani said.
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