Heavy firing was reported in Adhimiyah, a mainly Sunni district of Baghdad, within half an hour of Saddam Hussein's death sentence being announced on Sunday morning.
Several mortarshells also reportedly landed near the Abu Hanifa mosque in Adhimiya. The mosque is a focus for Sunni armed groups in the area.
Before the verdict was announced, Iraq's army imposed a complete curfew in Baghdad, in Diyala province, a mainly Sunni region and around Tikrit, Saddam's hometown.
In Tikrit as many as 1,000 people defied the curfew and carried pictures of the former president through the streets.
Some Sunnis there declared the court a product of the U.S. "occupation forces" and decried the verdict.
"By our souls, by our blood we sacrifice for you Saddam", they shouted. "Saddam your name shakes America."
Kurds and Shias celebrate
But while Iraq's Sunnis reacted angrily to the verdict, Iraq's other sects and ethnic groups have began celebrating.
Iraq's Shia who made up over half of Iraq's population have begun holding impromptu celebrations in Najaf and other cities to mark Saddam's sentencing.
Over 100,000 Iraqi Shias were killed in 1991 after attempting to overthrow Saddam's predominantly Sunni government.
Shias in Najaf have poured into the streets to celebrate
In Sadr City, a mainly Shia area of Baghdad, people celebrated in the streets, calling out: "Where are you Saddam? We want to fight you."
A jubilant crowd of young men carried pictures of radical Shia cleric Muqtada al-Sadr and handed out sweets to children.
In the streets of Dujail, a city of 84,000 on the river Tigris, people celebrated as the verdict was read out and then burned pictures of Saddam.
Iraq's four million ethnic Kurds are also expected to celebrate the sentence.
Saddam is also due to stand trial for the 1988 Anfal campaign which killed more than 200,000 Kurds.