US President Donald Trump has threatened to hit 52 Iranian sites "very hard" if Iran attacked Americans or American assets following a US raid on Friday that killed the head of the Quds Force, Qassem Soleimani, and an Iraqi militia leader.

Showing no sign of an effort to ease tensions in the region, Trump took to Twitter to warn that the US had "targeted 52 Iranian sites" and that some were "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!" Trump said.

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The 52 targets represented the 52 Americans who were held hostage in Iran for 444 days after being seized at the US embassy in Tehran in November 1979, he added.

Tensions have escalated since Friday, when the US killed Iranian commander Soleimani and top Iraqi paramilitary chief Abu Mahdi al-Muhandis in a drone attack on their convoy as it drove out of Baghdad's international airport.

Several rockets fell in and around Baghdad on Saturday night, including inside the capital's heavily-fortified Green Zone and the Balad airbase housing US troops.

No casualties were reported in the rocket attacks, which were confirmed by US military spokesman, Colonel Myles B Caggins III. He said no troops had been injured but Iraqi civilians could have been harmed.

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.... — Donald J. Trump (@realDonaldTrump) January 4, 2020

The Green Zone is the high-security enclave where the US embassy is based.

Al Jazeera's Osama Bin Javaid, reporting from Baghdad, said none of the projectiles landed inside the embassy compound.

"According to Iraqi security forces, the projectiles landed in the celebration areas inside the Green Zone," he said.

A pair of Katyusha rockets then hit the Balad airbase north of Baghdad, where American troops are based, security sources and the Iraqi military said.

Security sources reported blaring sirens and said surveillance drones were sent above the base to locate the source of the rockets.

There was no immediate claim of responsibility.

The US embassy in Baghdad, as well as the 5,200 American troops stationed across the country, have faced a spate of rocket attacks in recent months that Washington has blamed on Iran and its allies in Iraq.

Last month, one attack killed an American contractor working in northern Iraq, prompting retaliatory US air raids that killed 25 fighters close to Iran.

Iraqi Prime Minister Adel Abdul Mahdi attended the funeral ofQassem Soleimani and Abu Mahdi al-Muhandis, who were killed on Friday [Thaier al-Sudani/Reuters]

Escalating tensions

Gholamali Abuhamzeh, a senior commander of the Islamic Revolutionary Guard Corps (IRGC), said Tehran would punish Americans "wherever they are in reach", and raised the prospect of possible attacks on ships in the Gulf.

Iraq's Kataib Hezbollah militia warned Iraqi security forces to stay away from US bases in Iraq, "by a distance not less than a thousand metres starting Sunday evening," reported Lebanese al-Mayadeen TV, which is close to Lebanon's Hezbollah.

On Friday, Iran's Supreme Leader Ali Hosseini Khamenei said Soleimani's death would intensify Tehran's resistance to the US and Israel.

With security worries rising after Friday's raid, the NATO alliance and a separate US-led mission suspended their programmes to train Iraqi security and armed forces, officials said.

"The safety of our personnel in Iraq is paramount. We continue to take all precautions necessary," acting NATO spokesman Dylan White said in a statement.

The US has been an ally of the Iraqi government since the 2003 US invasion to overthrow leader Saddam Hussein, but Iraq has become more closely allied with Iran.

The top candidate to succeed al-Muhandis, Hadi al-Amiri, spoke over the dead militia commander's coffin: "The price for your noble blood is American forces leaving Iraq forever and achieving total national sovereignty."

The Iraqi parliament is convening an extraordinary session during which a vote to expel US troops could be taken as soon as Sunday. Many Iraqis, including opponents of Soleimani, have expressed anger at Washington for killing the two men on Iraqi soil and possibly dragging their country into another conflict.

Soleimani, 62, was Iran's pre-eminent military leader - head of the IRGC's overseas Quds Force and the architect of Iran's spreading influence in the Middle East.

Al-Muhandis was the de facto leader of Iraq's Popular Mobilisation Forces (PMF), an umbrella body of paramilitary groups.

A PMF-organised procession carried the bodies of Soleimani and al-Muhandis, and others killed in the US attack, through Baghdad's Green Zone.

Prime Minister Adel Abdul Mahdi also attended. Abdul Mahdi's office later said he received a phone call from Saudi Crown Prince Mohammed bin Salman and they "discussed the difficult conditions facing Iraq and the region".