TENS of thousands of mourners have accompanied a casket carrying the remains of the General Qasem Soleimani through two major Iranian cities.

It came as part of a grand funeral procession for the commander killed by an American drone strike amid soaring tensions between Iran and the US.

President Donald Trump has threatened to bomb 52 sites in Iran if it retaliates by attacking Americans.

The US Embassy in Saudi Arabia separately warned Americans "of the heightened risk of missile and drone attacks."

Meanwhile, Iran vowed to take an even-greater step away from its unravelling nuclear deal with world powers as a response to General Soleimani's death.

The leader of Lebanon's Hezbollah group said on Sunday that America's military in the Middle East region - including US bases, warships and soldiers – are fair targets following the killing of Iran's top general.

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READ MORE: These are the profound implications of the killing of Qasem Soleimani

Hassan Nasrallah said evicting US military forces from the region is now a priority.

"The suicide attackers who forced the Americans to leave from our region in the past are still here and their numbers have increased," Nasrallah said in a televised speech.

The US drone strike killing General Soleimani in Iraq Friday escalated the crisis between Tehran and Washington after months of trading attacks and threats that put the wider Middle East on edge.

The conflict is rooted in Trump pulling out of Iran's nuclear accord.

Iraq's parliament voted on Sunday to expel the US military from the country.

The resolution specifically called for an end to an agreement in which Washington sent troops to Iraq more than four years ago to help in the fight against the Islamic State group.

The US has some 5,000 troops deployed in different parts of Iraq.

After thousands in Baghdad on Saturday mourned General Soleimani and others killed in the strike, authorities flew the general's body to the south-western Iranian city of Ahvaz.

An honour guard stood by early on Sunday as mourners carried the flag-draped coffins of General Soleimani and other Guard members off the Tarmac.

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The caskets then moved slowly through streets choked with mourners wearing black, beating their chests and carrying posters with General Soleimani's portrait.

Demonstrators also carried red Shi'ite flags, which traditionally both symbolise the spilled blood of someone unjustly killed and call for their deaths to be avenged.

Officials brought General Soleimani's body to Ahvaz, a city that was a focus of fighting during the bloody 1980-88 war between Iraq and Iran, in which he slowly grew to prominence.

After that war, General Soleimani joined the Guard's newly formed Quds, or Jersualem, Force, an expeditionary force that works with Iranian proxy forces in countries like Iraq, Lebanon and Yemen.

Authorities then took General Soleimani's body to Mashhad.

His remains will go to Tehran and Qom on Monday for public mourning processions, followed by his hometown of Kerman for burial on Tuesday.

This marks the first time Iran honoured a single man with a multi-city ceremony.

General Soleimani will lie in state at Tehran's Musalla mosque on Monday.

It is unclear how or when Iran may respond but any retaliation is likely to come after three days of mourning declared in both Iran and Iraq.

Iranian officials planned to meet on Sunday night to discuss taking a fifth step away from its 2015 nuclear deal with world powers, one that could be even greater than planned, Foreign Ministry spokesman Abbas Mousavi told journalists.