Several blasts shook the Baghdad area hours after a huge funeral procession for a top Iranian general killed by a US air strike on Thursday.
A projectile hit the Green Zone near the US embassy while several more were fired north of the Iraqi capital at Balad air base, which houses US forces.
Nobody was hurt in the attacks, Iraqi security sources say.
Iranian leaders have vowed to avenge the killing of Qasem Soleimani, who was regarded as a terrorist by the US.
Saturday’s funeral procession through Baghdad and Iraq’s Shia Muslim holy cities precedes the return of his remains to Iran.
Iraqis were also mourning the death of Abu Mahdi al-Muhandis, an Iraqi who commanded the Iranian-backed Kataib Hezbollah group and was killed along with Soleimani.
In another development, the group issued a warning to Iraqi security forces to “stay clear of American bases by a distance not less [than] 1,000m (0.6 miles) starting Sunday evening”, al-Mayadeen TV reported.
In response to Iranian threats of revenge, the US has sent 3,000 more troops to the Middle East and advised its citizens to leave Iraq.
At least one rocket or mortar round hit Celebration Square in the Green Zone while another exploded in the city’s Jadria area, Iraqi security sources say.
After two rockets hit Balad airbase, surveillance drones were sent up to locate the source, AFP news agency reports.
No group said it had carried out the attacks. Pro-Iranian militants have been blamed for other recent rocket attacks on US interests in Iraq.
Waving Iraqi and militia flags and chanting “Death to America”, mourners walked behind the coffins from Al Muthana Airport to the gate of the Green Zone on Saturday.
Some mourners carried portraits of Soleimani while others held portraits of Iran’s Supreme Leader, Ayatollah Ali Khamenei.
Later, the procession left for the holy cities of Karbala and Najaf.
Some Iraqis, conversely, celebrated in Baghdad’s streets at the news of Soleimani’s death. He was accused of orchestrating violent crackdowns on peaceful pro-democracy protests there in recent months.
Reports say the bodies of Soleimani and four other Iranians killed in the air strike will be flown on Saturday evening to Iran, which has declared three days of mourning for the assassinated general. His funeral in Iran is to be held on Tuesday.
Its leaders have pledged to avenge the death of the man who led the Quds Force, an elite unit of the Iranian Revolutionary Guard.
Soleimani, 62, was widely seen as the second most powerful figure in Iran after Ayatollah Khamenei. The Quds Force reported directly to the ayatollah, and Soleimani was hailed as a heroic national figure.