"We are with you," they chanted as they waved their hands in unison during the outpouring of grief at a rally in Tehran's Palestine Square, an AFP correspondent reported.

Soleimani was killed on Friday in a US air strike outside Baghdad international airport that shocked the Islamic republic and sparked fears of a new war in the Middle East. He was 62.

One of Iran's most popular public figures, Soleimani was head of the Quds Force that oversaw the foreign operations of the Islamic Revolutionary Guard Corps.

Iran's supreme leader Ayatollah Ali Khamenei vowed "severe revenge" and declared three days of mourning on Friday following the news of his death.

At Saturday's rally in Tehran, men held up placards that called for "revenge" and black-clad women clutched portraits of Soleimani and Khamenei.

One man wearing a mask climbed onto a stone monument holding burning US and Israeli flags as others chanted "Death to America".

"Our response will definitely be beyond launching some missiles or destroying some American bases," said Milad Najafi, one of the mourners.

"In fact, I think our revenge will be the annihilation of Israel," the student told AFP.

Another mourner, Ali Gholinam, paid tribute to Soleimani as "the greatest man we had".

"They took him not only from Iran but from the 'Resistance Front'," he said, referring to Iran's allies in parts of the region including the Palestinian territories.

"The 'Resistance Front' members are now mourning this great man," he told AFP.

"I don't know what the response could be, but whatever it may be, it must be proportionate."

Soleimani's remains are due to be returned to Iran on Sunday ahead of ceremonies in Ahvaz, Tehran, Mashhad and Qom.

The slain general is expected to be laid to rest in his hometown of Kerman on Tuesday.