Some observers believe that Mr. Allawi, who is a secular Shiite, will have great difficulty cobbling together the necessary support and that Mr. Maliki may be able to return as prime minister.

“His problem is that while he is a pragmatist who could make a deal with the Kurds and some Shiite factions, one of his main constituencies are Sunni Arab nationalists who would not countenance an alliance with the Kurds, unless the Kurds made impossible concessions on Kirkuk and other disputed areas,” said Joost Hiltermann of the International Crisis Group. One result, he said, could be that the main Shiite parties could regroup and form a government similar to this one.

If Mr. Allawi failed to form a government, that task would fall to Mr. Maliki, who would be likely to seek an accommodation with the Iraqi National Alliance of Mr. Sadr.