The head of forensic medicine in Kerman, Abas Amian, said authorities had identified 50 people who were killed in the crush, the causes of which are as yet unknown, according to Tasnim news agency on Tuesday.
Videos circulating on social media allegedly showed several bodies lying on the floor, some with their faces purposefully covered over with jackets, reported Efe news.
The head of Iran's Emergency Center Hossein Kolivand said hundreds of people had been injured.
Many thousands of mourners packed the streets of the late general's home town ahead of his burial following similar displays of mass mourning in Tehran on Monday.
His burial was delayed by the stampede.
Soleimani's death on Friday in a United States drone strike outside Baghdad's international airport marked a considerable escalation in tensions between Washington and Tehran.
As the head of the elite Quds Force, a branch of the Islamic Revolutionary Guards Corps, Soleimani had for years wielded his country's influence across the wider Middle East, strengthening Shia militias from Lebanon to Iraq and coming to the aid of Tehran's allies, like Bashar Al Assad in Syria.
Iran's Supreme Leader Ali Khamanei led funeral prayers for the man widely regarded as the country's second most powerful figure on Monday.
US President Donald Trump has warned that any military retaliation from Iran would be met with American strikes.
Iranian lawmakers on Tuesday voted to designate the Pentagon and the US Army as a terrorist organization.
Iran had previously only considered the US Central Command (CENTCOM) as a terrorist organization a measure that came in response to Washington's designation of the IRGC as a terror group.
Parliamentary speaker Ali Larijani said Soleimani's killing had been a "brutal act" by Trump.
"The Iranian people will not pardon him."
There were cries of "Death to America" when lawmakers approved a financial package worth $223 million to the IRGC.
The head of the elite military wing in Iran, Hossein Salami, said the US would "lament its error" and vowed to oversee the expulsion of US troops from the Middle East.
There was confusion about the future of American troops in the US on Monday when the international coalition against the Islamic State released a statement suggesting soldiers would begin to "move out" of the region.
It was later contradicted by the Pentagon.
( With inputs from IANS )