The US, UN, Iran and Iraq's own Shi'ite clergy have pushed hard for politicians to come up with an inclusive government to save the country as Sunni insurgents bear down on Baghdad.
But with Shi'ites failing to name a prime minister, Sunnis and Kurds refused to return from recess at the parliamentary chamber in the fortified "green zone" where they were meeting for the first time since an election in April.
Parliament is not likely to meet again for at least a week, leaving the country in a state of political limbo and Mr Maliki clinging to power as a caretaker, rejected by Sunnis and Kurds.
Sunni parties said they would not put forward their candidate for speaker until the Shi'ites pick a premier. The Kurds have also yet to nominate a president.