A rocket has fallen near the US embassy in Baghdad - hours after mourners chanted "death to America" over the killing of Iran's top general in an airstrike.
There were no casualties after the rocket fell near the embassy compound in the Iraqi capital's green zone, police sources told Reuters.
Meanwhile, two Katyusha rockets have fallen near Iraq's Balad air base, which houses US forces. No casualties have been reported following this incident.
Separately, mortar has fallen in Baghdad's Jadriya neighbourhood - with police sources telling Reuters that five people have been wounded.
The Iraqi military said in a statement after the strikes: "Several rockets targeting Celebration Square and the Jadriya area in Baghdad, and the Balad air base in Salahuddin province, with no loss of life. Further details to come."
The UK's Defence Secretary Ben Wallace said two Royal Navy ships will return to accompanying commercial shipping through the Strait of Hormuz following the death of Major General Qassem Soleimani.
The statement read: "Yesterday I spoke to my US counterpart Secretary Esper and we urge all parties to de-escalate the situation. During the last few months US forces in Iraq who are based in Iraq at the invitation of the Iraqi government have been repeatedly attacked by Iranian backed militia.
"General Soleimani has been at the heart of the use of proxies to undermine neighbouring sovereign nations and target Iran's enemies. Under international law the United States is entitled to defend itself against those posing an imminent threat to their citizens.
"I have instructed preparation for HMS Montrose and HMS Defender to return to accompanying duties of the Red Ensign Shipping in the Strait of Hormuz. The government will take all necessary steps to protect our ships and citizens at this time."
Iraq's Kataib Hezbollah militia has warned the country's security forces to stay at least 1km from US bases starting Sunday evening, the Middle Eastern news service Mayadeen TV reports.
Iran has said it will punish Americans within reach of the country after Maj Gen Soleimani , head of the country's elite Quds force and mastermind of its regional security strategy, was killed in a US airstrike on his motorcade early on Friday near the Iraqi capital's international airport.
Iraq's prime minister has declared three days of national mourning for those who were killed in the airstrike.
A funeral procession took place on Saturday for Maj Gen Soleimani and Iraqi militant leaders, including paramilitary chief Abu Mahdi al Muhandi, and eight others who died.
Mourners - mostly men in black military fatigues - carried Iraqi flags and the flags of Iran-backed militias who are fiercely loyal to Maj Gen Soleimani.
Iraq's foreign minister Javad Zarif tweeted on Saturday: "24hrs ago, an arrogant clown - masquerading as a diplomat - claimed people were dancing in the cities of Iraq.
"Today, hundreds of thousands of our proud Iraqi brothers and sisters offered him their response across their soil.
"End of US malign presence in West Asia has begun."
The death of the top general has increased global tensions, with Iran vowing harsh retaliation while US President Donald Trump said he ordered the strike to prevent conflict.
Mourners at the general's funeral procession, many in tears, marched alongside militia vehicles in a solemn procession which began at the Imam Kadhim shrine, one of Shia Islam's most revered sites.
Chants of "No, no, America" and "Death to America, death to Israel" were heard, as well as "America is the Great Satan".
Two helicopters hovered over the procession, which was attended by Prime Minister Adel Abdul-Mahdi and leaders of Iran-backed militias.
As the funeral march took place, Tasnim news agency quoted a senior Revolutionary Guard commander saying Iran will punish Americans wherever they are within reach of the country.
General Gholamali Abuhamzeh said Iran had identified 35 US targets in the region, including in Tel Aviv and ships in the Gulf.
"The Strait of Hormuz is a vital point for the West and a large number of American destroyers and warships cross there," he said.
"Vital American targets in the region have been identified by Iran since long time ago.
"Some 35 US targets in the region as well as Tel Aviv are within our reach."
In the hours after the airstrike, Iranian defence minister Amir Hatami threatened "crushing revenge" and Iran's supreme leader, Ayatollah Ali Khamenei, said there would be "harsh retaliation".
Iranian President Hassan Rouhani added: "Soleimani's martyrdom will make Iran more decisive to resist America's expansionism and to defend our Islamic values."
On Friday, Mr Trump said the US carried out the airstrike because Maj Gen Soleimani had been planning "imminent and sinister attacks on US diplomats and military personnel".
In an address from his Mar-a-Lago resort in Florida, Mr Trump said: "What the US did yesterday should have been done long ago - a lot of lives would have been saved.
"We took action last night to stop a war. We did not take action to start a war."
An official with the US-led coalition in Iraq said operations have been scaled back and "security and defensive measures" have been boosted at bases hosting coalition forces.
An extra 3,000 US troops have been dispatched to neighbouring Kuwait.
Iraq - a close US and Iran ally - condemned the airstrike and called it an attack on its national sovereignty.
Its parliament will meet for an emergency session on Sunday as it comes under pressure to expel the 5,200 American troops based in the country to help prevent an Islamic State (IS) resurgence.
The Pentagon has said Maj Gen Soleimani, 62, "orchestrated" attacks on coalition bases in Iraq over the past few months and approved the attacks on the US embassy in Baghdad earlier this week.
Iran's second most powerful person after the supreme leader, Maj Gen Soleimani headed the overseas arm of the Revolutionary Guards, the Quds Force, and was the spearhead of Iran's growing military influence in the Middle East.
But Mr Trump declared Maj Gen Soleimani's "reign of terror" was over, adding the general had "made the death of innocent people his sick passion".
Mr Trump added: "I've deep respect for the Iranian people - they are a remarkable people with an incredible heritage and unlimited potential.
"We do not seek regime change.
"However, the Iranian regime's aggression in the region, including the use of proxy fighters to destabilise its neighbours, must end and it must end now."
The US embassy in Baghdad has urged American citizens to depart Iraq immediately "via airline while possible, and failing that, to other countries via land".
There are concerns foreign prisoners in Iran will be affected by the repercussions, with the husband of British woman Nazanin Zaghari-Ratcliffe, who has been imprisoned there since 2016, saying it was a setback for her situation.
Richard Ratcliffe told Sky News he spoke to his wife from prison on Saturday morning, saying all the foreign prisoners were "shocked and worried" and it is "very ominous" for American prisoners.
"It's a setback for any further rapprochement," he said.
"Nazanin is held by the Revolutionary Guard, they're not good guys but they're now angry, not good guys."
Britain's foreign office updated its travel advice on Saturday morning, advising against all travel to Iraq, except the Kurdistan region where only essential travel should take place.