The body of Iranian military commander Qasem Soleimani, who was killed in Iraq in a US military strike, was returned to Iran on Sunday and driven through thousands of mourners, the official IRIB news agency reported.

Soleimani, the architect of Tehran's overseas clandestine and military operations as head of the Revolutionary Guards Quds Force, was killed on Friday in a US drone strike on his convoy at Baghdad airport.

Read more: Qasem Soleimani — the general who became an Iran icon by targeting US

While many Iranians have rallied to show grief over the death of Soleimani, regarded as the country's second most powerful figure after Supreme Leader Ayatollah Ali Khamenei, others worry his death might push the country to war with a superpower.

US President Donald Trump on Saturday threatened to hit 52 Iranian sites very hard if Iran attacks Americans or US assets.

Khamenei promised harsh revenge and declared three days of mourning on Friday.

Soleimani's body was flown to the city of Ahvaz in southwest Iran.

IRIB posted a video clip of a casket wrapped in an Iranian flag being unloaded from a plane as a military band played.

Thousands of mourners dressed in black marched through the streets of Ahvaz beating their chests in live footage aired on state TV.

Soleimani's casket was driven amidst the large crowds on the back of a truck.

The body of Iranian-backed Iraqi militia leader Abu Mahdi al-Muhandis, who was killed in the attack with Soleimani, was also flown to Ahvaz, according to IRIB.

Read more: Ceremonies to honour general killed by US begin in Iran's Ahvaz

Tens of thousands of people marched in Iraq on Saturday to mourn Soleimani and al-Muhandis, chanting “Death to America”.

Iranian parliamentarians also chanted “Death to America” in a parliamentary session shown on state TV on Sunday.

Oman has called on the United States and Iran to seek dialogue to ease tensions, Oman News Agency reported on Sunday.

Oman, which maintains friendly ties with both the United States and Iran, has previously been a go-between for the two countries.

On Saturday evening, a rocket fell inside Baghdad's heavily fortified Green Zone near the US embassy, another hit the nearby Jadriya neighbourhood and two more were fired at the Balad air base north of the city, but no one was killed, the Iraqi military said in a statement.

There was no immediate claim of responsibility.