Tens of thousands of mourners clad in black have filled the streets of Mashhad and Ahvaz to pay their respects to Qassem Soleimani, the country's most powerful and revered military commander who was assassinated by a US air strike in Iraq.

Soleimani's remains were flown to the southwestern city of Ahvaz early on Sunday, two days after his killing triggered a dramatic escalation of tensions in the Middle East.

Several others were also killed in Friday's strike on a convoy at Baghdad airport, including the Iranian-backed Iraqi militia leader Abu Mahdi al-Muhandis.

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In live footage aired on Sunday on Iranian state television, tens of thousands of mourners marched through Ahvaz holding up portraits of Soleimani, seen as a hero for his role in the Iran-Iraq war in the 1980s and for spearheading Iran's Middle East operations as chief of the Iranian Revolutionary Guard Corps's (IRGC) overseas forces.

The footage showed crowds thronging Mollavi Square with flags in green, white and red - depicting the blood of "martyrs" - men and women weeping as they beat their chests to the sound of chants.

The body of Soleimani arrived Sunday in Iran to throngs of mourners [Morteza Jaberian/Mehr News Agency via AP]

Authorities plan to take Soleimani's remains to the holy city of Mashhad later on Sunday, as well as Tehran and the holy city of Qom on Monday, for public mourning processions, then to his hometown of Kerman for burial on Tuesday.

Al Jazeera's Dorsa Jabbari, reporting from Mashhad, said mourners have gathered at the Imam Reza shrine where Soleimani's coffin would later be displayed.

"He is highly revered and loved. Many people say they can't believe he's gone. The whole country is in mourning," Jabbari said.

"Aside from the grief... there is a lot of anger and frustration. Iranians want their government and their military to respond. They want revenge."

Trump threatens to hit 52 Iranian sites

The assassination of Soleimani marks the most significant escalation in tensions between the US and Iran in recent years.

The friction is rooted in the 2018 US decision to pull out of a nuclear deal signed in 2015 between Iran and world powers. The landmark accord is likely to further unravel as Tehran is expected to announce as early as Sunday that it will take another step away from it in the wake of Washington's withdrawal and reimposition of punishing sanctions.

Following Soleimani's assassination, Iran's Supreme Leader Ayatollah Ali Khamenei warned of "harsh revenge" as he called for three days of national mourning while Iranian President Hassan Rouhani said Tehran's response to the killing would be long and drawn out.

Though it is unclear how or when Iran may respond, any retaliation is likely to come after the mourning period ends.

Luciano Zaccara, research coordinator in Gulf politics at Qatar University told Al Jazeera he believes Iran will not leave the death of Soleimani "unpunished" as he is a popular political figure in Iran.

"The leader and everybody inside Iran already promised that his death will be avenged; it would very difficult to believe that nothing is going to happen," Zaccara said.

"Iran has been bragging about their capacity to mobilise other groups outside Iran - Syria, Lebanon, Yemen. Having in mind the attack was conducted inside Iraq, [I assume] that the main target would be American interests in areas where there are American and Iranian troops like Syria or Lebanon or Iraq."

US President Donald Trump on Saturday threatened to hit 52 Iranian sites "very fast and very hard" if Iran retaliated and attacked US citizens or assets. Meanwhile, the US has dispatched another 3,000 troops to Kuwait, the latest in a series of deployments in the region in recent months.

In Iraq, where three days of mourning have also been declared, security forces were on high alert, according to Al Jazeera's Osama Bin Javaid.

Reporting from Baghdad, Bin Javaid said the burial of al-Muhandis would take place in the southern city of Najaf.

Meanwhile, tens of thousands of Iraqis marched on Saturday in several cities to mourn al-Muhandis and Soleimani.

In the 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 airbase north of the capital, but no one was killed, the Iraqi military said in a statement.

There was no immediate claim of responsibility.