Soleimani, who commanded the elite Quds Force, was responsible for building up Tehran's network of proxy armies across the Middle East. He was a pivotal figure in orchestrating Iran's long-standing campaign to drive US forces out of Iraq.
A senior Iranian official said Tehran was considering several scenarios to avenge his death. Other senior figures have said the Islamic Republic would match the scale of the killing when it responds, but that it would choose the time and place.
Tuesday's stampede broke out amid the crush of mourners, killing 56 people, state television said, raising the toll from 50 previously. More than 210 people were injured, an emergency services official told the semi-official Fars news agency.
"Today because of the heavy congestion of the crowd unfortunately a number of our
fellow citizens who were mourning were injured and a number were killed," emergency medical services chief Pirhossein Kolivand told state television.
Soleimani was a national hero to many Iranians, whether supporters of the clerical leadership or not, but viewed as a dangerous villain by Western governments opposed to Iran's arc of influence running across the Levant and into the Gulf region.
Iran's opponents say its proxies have fuelled conflicts, killing and displacing people in Iraq, Syria and beyond. Tehran says any operations abroad are at the request of governments and that it offers "advisory support".
Soleimani's body had been taken to Iraqi and Iranian cities before arriving in Kerman for burial.
Iran's parliament, meanwhile, has passed an urgent bill declaring the US military's command at the Pentagon and those acting on its behalf in Soleimani's killing as “terrorists," subject to Iranian sanctions.
The measure appears to be an attempt to mirror a decision by President Donald Trump
in April to declare the Revolutionary Guard a “terrorist organisation.” The US Defense Department used the Guard's designation as a terror organisation in the US to support the strike that killed Soleimani.