Several of the top contenders for the prime minister's job come from the same electoral list, the United Iraqi Alliance, a coalition that includes the country's two largest Shi'ite political parties, the Islamic Dawa Party and the Supreme Council for the Islamic Revolution in Iraq, known as SCIRI. Since the alliance has developed a strong lead in early election results, it is looking likely that one of its members will end up with the job.
But there are at least two main candidates within the alliance: Iraq's interim Vice President Ibrahim Jafari of the Dawa Party, and Adil Abdel Mahdi, the current finance minister and a senior member of SCIRI.
Even though the United Iraqi Alliance is perceived as a Shi'ite religious slate, neither man is a cleric. Mr. Jafari trained as a medical doctor in the northern city of Mosul, before going into exile during the time of Saddam Hussein. He lived in both Iran and Britain.
In an interview with VOA, Mr. Jafari downplayed his desire to become prime minister, saying his main goal had simply been holding democratic elections in Iraq.
"It is not important who is to become a prime minister," he said. "Personally, I did not put myself as a goal, as a target. My target is the election."
Mr. Jafari believes the Shi'ite alliance will end up with more than 50 percent of the votes, and, therefore, more than half of the seats in the transitional National Assembly. Early results from the Shi'ite-dominated south support that conclusion, although it is too soon to say what the final picture will look like.
Most Sunni Muslim parties boycotted the poll, and voter turnout is believed to have been much lower in Sunni regions than it was in the Shi'ite and Kurdish areas.
But several key Sunni groups have indicated that they might be willing to take part in drafting the constitution. Mr. Jafari welcomed that idea.
"Yes, not only in the constitution. I think Sunnis are a very important component in our society. So, I think we have to involve them in the new government, and we have to give them a main situation, very important, to share either a presidency, or the head of parliament, or, of course, several ministries should be involved by our brother Sunnis. Of course, at the same time, the constitution," he said.
Many Iraqi and American officials fear that completely sidelining the Sunnis from the political process could worsen the insurgency. Mr. Jafari said there can be a role in the political system for Sunnis who boycotted the election, but he ruled out including insurgents or terrorists.
"But they are not killing. Those who did any terrorism, and kill any person, no. This is a red line to me," he said.
One thing that key Sunni leaders have demanded is a timeline for the withdrawal of American troops and other international forces. Mr. Jafari says the multi-national troops will not leave, until the security situation allows it.
"Of course, the presence of multi-national forces, it is not a positive sign, because they are not Iraqi. But compare their presence with their absence," said Mr. Jafari. "Take into consideration our need to them for the security. I think, we have to accept them until we can depend on ourselves."
Some secular and Sunni Iraqis have expressed concern about the influence Iran might have over a government led by the United Iraqi Alliance. Many of its members, like Mr. Jafari, lived in Iran in exile at some point, and many have close ties to the government in Tehran.
Even though he downplayed his own desire for the prime minister's job, Mr. Jafari said the person who eventually leads Iraq should be a Shiite who can reach out, not only to Iraqi Sunnis, but also to neighboring Arab countries and the rest of the Islamic world, which is almost entirely Sunni.
"If we look into Islamic world, with exception of Iran, all the Islamic world is Sunni. We are the minority. It is the rule. … So, they are worried. What is going to be occurring [in] Iraq? So, we have to choose a person, a Shiite, that is either accepted [by] our brother Sunni, or at least they [will] not refuse him. You have to respect them," he continued. "You have to show them that we have a Shiite face accepted from you, or at least not refused. … If we can approach them, the Sunni inside Iraq and the Sunni outside Iraq, with a person who is accepted, I think we can solve the problem."
Mr. Jafari also had a message for the U.S. government, which has had bad relations with Iran.
"And to America, let me say something frankly. Please do not fear from election. You have to accept the election. Our people in the election [are] going to choose two groups: a group of leaders, and a group of friends. If you like to be, as Americans, to be friends of our people, please accept the result of the election," he said.
He said that if the Iraqi people have chosen a Shiite government, they will respect the United States more if it respects that choice.
The Bush administration has said it is for the Iraqis to decide the makeup of their future government, and that it will continue to support the Iraqis as they move to draft a constitution and hold new elections. Vice President Dick Cheney said Sunday in a television interview in Washington that he has confidence in Grand Ayatollah Ali al-Sistani's commitment to include minority Sunni Muslims in any future government.