A fresh air strike hit pro-Iran fighters in Iraq early Saturday, as fears grew of a proxy war erupting between Washington and Tehran a day after an American drone strike killed a top Iranian general. It came hours ahead of a planned a mourning march for Iranian Quds Force commander Qasem Soleimani and Iraqi paramilitary heavyweight Abu Mahdi al-Muhandis, slain in a precision drone strike by the US in Baghdad on Friday.

The assassination was the most dramatic escalation yet in spiralling tensions between Iran and the US, which pledged to send more troops to the region even as US President Donald Trump insisted he did not want war. The killing was the most dramatic escalation yet in spiralling tensions between the US and Iran, which Iraqis fear could play out in their homeland.

Almost exactly 24 hours later, a new strike targeted a convoy belonging to the Hashed al-Shaabi, an Iraqi paramilitary network whose Shia-majority factions have close ties to Iran, the group said in a statement.

It did not say who was responsible but Iraqi state television reported it was a US air strike. A police source told AFP the bombardment north of Baghdad left "dead and wounded," without providing a specific toll. There was no immediate comment from the US.

The assassination of Soleimani, who had led the Islamic Revolutionary Guards Corps' foreign operations branch and was Iran's pointman on Iraq, rattled the region.

US officials said the 62-year-old, who had been blacklisted by the US, was killed when a drone hit his vehicle near Baghdad's international airport.

A total of five Revolutionary Guards and five Hashed members were killed in the strike.

Their bodies were to be taken through an elaborate mourning procession on Saturday, beginning with a state funeral in Baghdad and ending in the holy shrine city of Najaf.

The bodies of the Guards would then be sent to Iran, which had declared three days of mourning for Soleimani.

US President Donald Trump hailed the operation, saying he decided to "terminate" Soleimani after uncovering he was preparing an "imminent" attack on US diplomats and troops.

He insisted Washington did not seek a wider conflict, saying: "We took action last night to stop a war. We did not take action to start a war."

But the Pentagon said hours later that 3,000 to 3,500 troops from the 82nd Airborne Division's Global Response Force would be dispatched to Kuwait.

A US official had told AFP that some of the 750 troops already sent from that unit had arrived in Baghdad and would reinforce security at the US embassy there.

Some 14,000 other troops have already been deployed as reinforcements to the Middle East this year, reflecting steadily growing tensions with Iran.

There are approximately 5,200 US troops deployed across Iraq to help local forces ensure a lasting defeat of militants.

Pro-Iran factions in Iraq have seized on Soleimani's death to push parliament to revoke the security agreement allowing their deployment on Iraqi soil.

Lawmakers are set to meet on Sunday for an emergency session on the strike and are expected to hold a vote.

Paramilitary figures in Iraq including US-blacklisted Qais al-Khazaali and militiaman-turned-politician Moqtada Sadr called on their fighters to "be ready" after Friday's strike.

And Lebanon's Tehran-backed Shia movement Hezbollah warned of "punishment for these criminal assassins." Soleimani had long been considered a lethal foe by US lawmakers and presidents, with Trump saying he should have been killed "many years ago."

The last straw was an attack by a pro-Iran mob on the US embassy in Baghdad this week, where demonstrators burned the entrance to the compound and besieged diplomats inside.

Iraqi premier Adel Abdel Mahdi warned the strike would "spark a devastating war in Iraq" as President Barham Saleh pleaded "voices of reason" to prevail.

Meanwhile, tens of thousands of Iraqis, many chanting "Death to America", Saturday mourned a top Iranian commander and others killed in a US drone attack that sparked fears of a regional proxy war between Washington and Tehran.

The killing of Iran's Major General Qasem Soleimani on Friday was the most dramatic escalation yet in spiralling tensions between Iran and the United States, which pledged to send thousands more troops to the region.

Iraqi political leaders and clerics attended the mass ceremony to honour 62-year-old Soleimani and the other nine victim of the pre-dawn attack on Baghdad international airport.

US President Donald Trump said he had decided to "terminate" Iran's military mastermind to prevent an "imminent" attack on US diplomats and troops.

"We took action last night to stop a war," he insisted. "We did not take action to start a war."

But a furious Iran has vowed revenge for the killing of Soleimani, the chief architect of its military operations across the Middle East.

"The response for a military action is a military action," Iranian ambassador to the United Nations Majid Takht Ravanchi told CNN, calling the strike an "act of war".

"By whom, by when, where? That is for the future to witness."

In the hours after the strike, the US reached out to Iran, with which it has had no direct diplomatic ties for decades.

Switzerland, whose embassy in Tehran represents US interests, confirmed Saturday its charge d'affaires had on Friday been "informed of Iran's position and in turn delivered the message of the United States".

Iran's Revolutionary Guards said Washington had used "diplomatic measures" to urge Tehran to respond "in proportion" to the strike - a message Iran's foreign minister Mohammad Javad Zarif slammed as "foolish".

Iraqis worry the US strike could unleash a new wave of destabilisation for Iraq, which only two years ago announced it had defeated the Islamic State group.

Abdel Mahdi warned Friday it would "spark a devastating war in Iraq", while President Barham Saleh pleaded for "voices of reason" to prevail.

On Saturday, the Hashed said a new strike had hit a convoy of their forces north of Baghdad, with Iraqi state media blaming the US.

While praying over Muhandis's remains in Baghdad, top Hashed official Hadi al-Ameri pledged to avenge him by ousting US troops. "Be reassured that the price of your pure blood will be the departure of American troops from Iraq, forever," he said.