Baghdad residents interviewed by RFE/RL say such reconciliation is vital after years of brutal dictatorship, killings, and religious intolerance.
Rahid Sobhai Nasir is a Sunni Arab in his 30s who works as a carpenter at a building site. He says the animosity between Sunnis and Shi'a is a curse that sometimes results in needless killings.
He says Sunnis and Shi'a are both Arabs and Muslims and should unite in building a new country.
"There is no difference between Sunni and Shi'a," he says. "All of us are Iraqis, and God willing, we will have reconciliation and we will forget the past. What we have is the present, and we hope that every Iraqi will forget the past. Now we have to build a new future."
Nasir says the composition of the new interim Iraqi government offers hope that such reconciliation can occur.
Shi'a Muslims make up more than 60 percent of Iraq's 25 million people. Former Iraqi President Saddam Hussein was a Sunni by origin who purged the Shi'a from the ruling secular Ba'ath Party and excluded them from the bureaucracy and security forces.
Redha Taki is the head of the political department of the Supreme Council for the Islamic Revolution in Iraq (SCIRI), the best-organized Shi'a political party. He says the rivalry between Sunni and Shi'a Arabs in Iraq started much earlier than the establishment of the modern Iraqi state in 1932. Only now, he says, with the advent of democracy, do Shi'a and Sunnis have an opportunity to bury old fears and animosities.
"Iraqi Sunnis represented by their parties and sheiks and tribal leaders are pleased with the present structure of the [interim] government," Taki says. "The president of Iraq [Ghazi Ajil al-Yawir] is a Sunni, and there are Sunni ministers, and there are Sunnis in the army, though they thought they might be discriminated against. The hopes of those Sunnis who want the past to come back are hollow. This will never happen."
Taki notes that al-Yawir is an influential Sunni tribal chief. Prime Minister Iyad Allawi is a Shi'a Muslim and a former member of the Ba'ath Party who became one of the staunchest opponents of Saddam Hussein. The new foreign minister is a Kurd.
Taki also says there are some practical steps being taken by SCIRI that might further the cause of reconciliation. This week, he says, SCIRI met with members of the Islamic Scholars Association. The association is a popular Sunni organization that strongly opposes the presence of U.S. troops in Iraq and which has refused to cooperate with any government set up during the occupation.
Taki says SCIRI and the association discussed the situation in Al-Fallujah. Sunni clerics told SCIRI they are not happy with what is going on in Al-Fallujah, a hotbed of Sunni resistance, and are trying to find a peaceful solution to tensions in the city. In April, the central government effectively lost control of the town.
Taki says there are some Sunnis who still think God has given them the right to govern the country. However, he says democratic practices will not allow the minority to rule the country as it did before.
Saddam Hussein's rule has left deep scars and divisions in Iraqi society. Many people say it will be impossible to speak about justice and reconciliation without first having a trial of the former dictator.
Baghdad resident Daud Akhmad Hasin, an engineer, says reconciliation can never extend to Saddam Hussein.
"Saddam cannot ever be forgiven. It is impossible because of the atrocities that he committed," Hasin says. "He committed crimes against the Iraqi people. And not only the Iraqis, but also the surrounding countries. He attacked Iran. He attacked Kuwait."
Hasin says Hussein's crimes are known to everyone. "People who make mistakes should be forgiven, but not Saddam and his accomplices. They didn't kill people by mistake," says Hasin.
A middle-aged man, Ali, says that for the sake of reconciliation and security, everyone should be forgiven. He says his family wasn't mistreated during the former regime and that he has no idea why Hussein should not be forgiven, too.
"Yes, we can forgive [Hussein]," Ali says. "The man did nothing to the Iraqis. We can give him a new start and forgive him. We don't have anything against him."
But Ali is the exception, not the rule.
Redha Taki from SCIRI says his two sisters were killed by the regime in 1983 because they were Shi'a. He himself says he had to flee to Iran.
Taki says there are three ways to classify supporters of the former regime: "There are three groups in the former Ba'ath Party. One group consists of Ba'athists who have the blood of innocent people on their hands, of whom there are a little bit more than 200 people. These people should be tried and punished."
Saddam belongs to this group.
He says the second group consists of those who joined the Ba'ath Party seeking better jobs.
Then there are people who became Ba'athists because they believed in the party's ideas but who were disappointed by the reality.
Taki says those who fall into the latter two groups should be treated differently from Saddam Hussein and other close advisers in his regime.
(Click here for the other four parts in this series, along with complete coverage and analysis of events in Iraq at RFE/RL's dedicated "The New Iraq" webpage.)