Iraq's Foreign Ministry has summoned the US ambassador to the country due to "repeated US air strikes".
It follows the killing of Major General Qassem Soleimani, head of Iran's elite Quds force and mastermind of its regional security strategy, in an airstrike in Baghdad on Friday.
His killing, and that of Iraqi militant leaders including paramilitary chief Abu Mahdi al Muhandi and eight others, has increased global tensions, with Iran vowing harsh retaliation while US President Donald Trump said he ordered the strike to prevent conflict.
During a funeral procession on Saturday for the men in Baghdad, mourners - mostly men in black military fatigues - carried Iraqi flags and the flags of Iran-backed militias who are fiercely loyal to Soleimani.
The mourners, 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 Iraqi Prime Minister Adel Abdul-Mahdi and leaders of Iran-backed militias.
On Sunday, Iraq's foreign ministry denounced the airstrikes as a "blatant" violation of sovereignty and a breach of the agreement between Iraq and the US-led coalition.
It said Iraqi soil should not be used to attack its neighbouring countries and Iraq's parliament parliament passed a resolution asking the government to end the presence of foreign troops in the country and ensure they do not use its land, air and waters for any reason.
Parliament resolutions are non-binding to the government, but Iraqi Prime Minister Adil Abdul Mahdi earlier called on MPs to end foreign troop presence.
The US-led coalition said it has paused the training support of Iraqi military because of repeated rocket attacks, and added it is fully committed to protecting Iraqi bases housing its troops.
Earlier, US President Donald Trump claimed he had a list of "52 Iranian targets" that would be "hit very fast and very hard" should Iran strike any Americans or US assets in retaliation for the killing of Soleimani.
"Iran is talking very boldly about targeting certain USA assets as revenge for our ridding the world of their terrorist leader who had just killed an American, & badly wounded many others, not to mention all of the people he had killed over his lifetime, including recently hundreds of Iranian protesters," the US president wrote on Twitter.
"He was already attacking our Embassy, and preparing for additional hits in other locations. Iran has been nothing but problems for many years.
"Let this serve as a WARNING that if Iran strikes any Americans, or American assets, we have targeted 52 Iranian sites (representing the 52 American hostages taken by Iran many years ago), some at a very high level & important to Iran & the Iranian culture, and those targets, and Iran itself, WILL BE HIT VERY FAST AND VERY HARD.
"The USA wants no more threats!"
....targeted 52 Iranian sites (representing the 52 American hostages taken by Iran many years ago), some at a very high level & important to Iran & the Iranian culture, and those targets, and Iran itself, WILL BE HIT VERY FAST AND VERY HARD. The USA wants no more threats!
— Donald J. Trump (@realDonaldTrump) January 4, 2020
Mr Trump went on to say that the US has recently spent "two trillion dollars on military equipment".
"We are the biggest and by far the BEST in the World! If Iran attacks an American Base, or any American, we will be sending some of that brand new beautiful equipment their way...and without hesitation!" he tweeted.
His comments came after a rocket fell near the US embassy in Baghdad.
There were no casualties after the rocket fell near the embassy compound in the Iraqi capital's green zone, police sources told Reuters.
Two Katyusha rockets have also 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.
Iran has said it will punish Americans within reach of the country.
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."
24 hrs 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. pic.twitter.com/eTDRyLN11c
— Javad Zarif (@JZarif) January 4, 2020
Following the funeral, 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.
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 claimed the US carried out the airstrike because Soleimani had been planning "imminent and sinister attacks on US diplomats and military personnel".
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 also been dispatched to neighbouring Kuwait.