The amnesty had been expected to be a key element in the government's efforts to coax Iraqis away from the anti-U.S. campaign, but the more limited offer is unlikely to dampen the violence.
Iraqi officials had earlier said the amnesty might extend to those who killed U.S. and other coalition troops. U.S. officials said an early draft contained ambiguous language on that issue, but later drafts ruled it out.
The announcement came as sporadic clashes continued in the holy Shiite city of Najaf, but fighting was largely calmed after two days of the most intense battles between U.S. forces and Shiite Muslim militiamen in months. The fighting Thursday and Friday spread to other Shiite communities and threatened to reignite a Shiite insurrection.
Much of the main fighting appeared over by Saturday afternoon.
Shiite leaders, joined by a U.N. official, met with aides to militant Shiite cleric Muqtada al-Sadr, whose militia was involved in the fighting, in an effort to mediate an end to the violence.
But CBS News Correspondent Kimberly Dozier reported Saturday from Baghdad that some religious and government officials there fear al Sadr has created a monster he can no longer control. And that his fighters may turn on him, too, if they think he is cooperating with the new Iraqi government, or the Americans.
And the amnesty was rejected immediately by al-Sadr. "This is a trivial and insignificant statement," said al-Sadr aide Ahmed al-Shaibany. "Amnesties are for criminals, but resistance is legitimate and does not need an amnesty."
In other developments:
Allawi's government has made putting down the insurgency a priority, though guerrilla attacks, as well as Iraqi and U.S. deaths, have not flagged since his government came to power in late June.
The amnesty had been intended to draw nationalist guerrillas to the side of Allawi's government and away from fighters using terrorist-style bombings.
Early drafts reportedly would have forgiven most people involved in the insurgency, but the law was apparently changed to exclude anyone who had killed.
"This amnesty is not for people ... who have killed. Those people will be brought to justice, starting from Zarqawi down to the person in the street," he said, referring to al Qaeda-linked Jordanian militant Abu Musab al-Zarqawi, whose followers have claimed responsibility for deadly suicide bombings.
The amnesty would forgive those who committed minor crimes between May 1, 2003, just after the fall of Saddam Hussein's regime, and Saturday, he said. Those eligible would need to turn themselves in over the next 30 days, he said.
Those eligible for the amnesty include people in possession of light arms and explosives, those who hid intelligence about terrorist groups and people who helped those groups commit crimes, Allawi said.
"This order has been established to allow our citizens to rejoin civil society and participate in the reconstruction of their country and the improvement of their lives, instead of wasting their lives pointlessly toward a lost cause," he said.
Meanwhile, Iraqi religious leaders tried to restore a ceasefire between al-Sadr's Mahdi Army militants and coalition and Iraqi forces that had shattered in two days of fighting that began Thursday.
The fighting in Najaf killed five U.S. service members, bringing to 16 the number of U.S. troops who died in Iraq in the first week of August.
Iraqi casualties from the fighting varied widely. Falah Muhana, a Health Ministry official in Najaf, said the city's hospitals reported 21 people killed and 121 injured during fighting in the city. The U.S. military said 300 militants were killed in Najaf, but Ahmed al-Shaibany, an al-Sadr aide in Najaf, said 36 militants had been killed. The militants often use their own health system so it is difficult to confirm their casualties.
Al-Sadr aides met in Baghdad on Saturday with Iraqi dignitaries and U.N. official Jamal Benomar.
Benomar said al-Sadr's group was prepared for an immediate cease-fire and had asked for a meeting between their group and Allawi and Iraqi President Ghazi al-Yawer.
Officials from the Supreme Council for the Islamic Revolution in Iraq — a top Shiite faction — arrived in Najaf on Saturday to mediate between al-Sadr, the local government and coalition forces, said Redha Taqi, a SCIRI official.
In Karbala, senior Shiite cleric Grand Ayatollah Mohammed Taqi al-Modaresi called for an immediate end to the violence.
In Najaf, U.S. warplanes flew overhead and American armored vehicles and Humvees blocked the main roads into the city on Saturday afternoon, but most streets appeared deserted. Sporadic explosions and gunfire echoed through the city, but the violence was far less than that of the previous days.
Najaf Gov. Adnan al-Zurufi on Friday gave insurgents 24 hours to leave the city.
On Saturday, it was unclear if militiamen were withdrawing. None were present outside al-Sadr's house, which is usually heavily guarded.
Allawi said more than 1,200 people had been arrested during the clashes — some of them followers of Saddam's regime, others common criminals released during Saddam's rule.
Operations to restore security in Najaf would continue, he said.
Friday's clashes were the fiercest seen in Najaf since the fall of Saddam Hussein, with U.S. helicopter gunships and fighter jets pounding insurgents hiding in a sprawling cemetery in the holy Shiite city.
On Saturday, the U.S. military said it had secured the cemetery. Marines also found weapons caches there, including bomb-making materials, rocket-propelled grenades, assault rifles and ammunition.
The fighting with al-Sadr's followers spread Friday to the Baghdad neighborhood of Sadr City and the southern cities of Amarah, Basra and Nasiriyah.