Both the Supreme Council and Dawa bring leverage to the internal negotiations. The Supreme Council fared far better in provincial elections in the south than Dawa but is dogged by a widely held perception that it is unduly influenced by Iran. Jafari, who returned from exile in London after the United States invaded Iraq in 2003, is seen as more independent, and his party has deep roots in the country. He was relatively popular during his tenure in the rotating presidency of the U.S.-appointed Governing Council in 2003, and although he is an Islamic activist, he is considered somewhat more moderate than some of his competitors in the Supreme Council.
"Whoever rules Iraq should represent Iraq as a nation, regardless of whether they are Sunni or Shiite," Jafari said in an interview last month. "He should be Iraqi first."

Ibrahim Jafari, 58, a physician and former exile, is one of four candidates being considered as the next prime minister of Iraq, officials say.
(Hadi Mizban -- AP)
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While the government's main task will be drafting a constitution, Jafari said it should first put down the insurgency. "We have to put security as our priority. If there is no security, there are no services, there is no business, there is no politics," he said.
The approach the government takes toward the insurgency could play a decisive role in deciding how to include Sunni Arab groups that boycotted the vote. Some of those groups have insisted they will not engage the government until the United States sets a timetable for a withdrawal of its 150,000 troops.
"The crux of the problem is the occupation," said Abdel-Salaam Kubeisi, a leader of the Association of Muslim Scholars, an influential Sunni Arab-led group that championed the call for a boycott.
"We all realize that under occupation, there is no chance for any legitimate government," he said in an interview Tuesday. "So whether it is Jafari or Allawi or Chalabi, they are all the same to us. They all came with the occupation."
U.S. officials have flatly rejected setting a deadline for a withdrawal, saying the departure of troops depends on progress in the training and deployment of Iraqi security forces.
Correspondent Doug Struck and special correspondents Bassam Sebti and Khalid Saffar contributed to this report.