A number of children were wounded in the attacks on the Shia district
At least six people have been killed in mortar attacks in Baghdad on the fifth anniversary of the city's capture by American forces.
The attacks, in the Sadr City district of the city, came as the capital observed a vehicle curfew.
Shia cleric Moqtada Sadr had called for a mass anti-American rally, but cancelled it amid security concerns.
It is five years since US troops pulled down a large statue of the late Saddam Hussein in the city centre.
Witnesses and officials told the BBC that one mortar exploded at a funeral wake, killing one person and wounding unknown others.
A second mortar landed on a building, killing five.
Baghdad's Green Zone, which houses diplomatic missions and much of Iraq's government, also came under mortar fire but there are no reports of injuries.
Cars and motorcycles have been banned from the streets until midnight (2100 GMT), the Iraqi government said.
People have been mostly staying at home, reports say.
Clashes overnight in Sadr City between Iraqi and US forces and militiamen loyal to the cleric left at least 12 people dead, medical workers said.
Moqtada Sadr had said that a one-million-strong protest was planned to mark the anniversary, but he called it off, saying he feared there could be bloodshed.
Gen Petraeus said Iraq's security improvement remains fragile
He also threatened to suspend a truce - credited with helping curb violence levels in Iraq since last year - by his powerful Mehdi Army militia.
"If necessary the ceasefire will be lifted in order to implement our aims, ideology, religion, principles, nationhood," a statement said.
On Monday, Iraq's prime minister threatened to exclude the radical Shia cleric's movement from politics unless he disbanded the Mehdi Army.
In recent weeks, Moqtada Sadr's followers have clashed with Iraqi government troops and US forces in southern Iraq and Baghdad, as the government tried to crack down on militias.
On Tuesday, the top US military leader in Iraq, Gen David Petraeus, told US Congress that any progress recently made in Iraq were "fragile and is reversible".
He recommended a suspension of US troop withdrawals after July to protect security gains made during the Iraq "surge", which saw an increase in US forces.
After the planned "drawdown" of about 20,000 troops, there should be a 45-day "period of consolidation and evaluation", Gen Petraeus said.