The first procession took place in Ahvaz, the main city in Iran's eight-year battle against the forces of the former Iraqi dictator Saddam Hussein which shaped Soleimani's future as an austere military tactician, the Tehran-based Press TV said in a report.
At noon, his remains were to be taken to the holy city of Mashhad and later to the capital, Tehran, reports Efe news.
In Ahvaz, thousands of people gathered to honour Soleimani among chants against the US, Israel and Saudi Arabia, according to the live broadcast on Iranian state television.
Iranian authorities have accused Washington's allies in the region, mainly Israel and Saudi Arabia, of instigating the January 3 attack that killed Soleimani and his son-in-law and Abu Mahdi al-Muhandis, the second-in-command of Iraq's Popular Mobilization Front (PMF), along with eight other people.
The remains of Muhandis and at least one other killed in the attack are also part of the funeral procession in Iran as they are mixed up with those of Soleimani and a DNA test is needed.
After the DNA test, the remains of the Iraqis will be returned to their country, where funeral ceremonies were also performed in Baghdad and other cities on Saturday.
The Iranian rites will continue on Monday in Tehran, where the main funeral ceremony will be held, and will end in Soleimani's southern hometown, Kerman.
Soleimani, 63, was the elite Quds Force chief in charge of Islamic Revolutionary Guard Corps operations outside Iran, and has been on the ground in Syria and Iraq supervising militias backed by Tehran.
The Quds Force holds sway over a large number of militias across the region ranging from Lebanon to Syria and Iraq.
Supreme Leader of Iran Ayatollah Ali Khamenei , as well as other political and military leaders of the country, have called for "harsh revenge" over the killing of the commander.
US President Donald Trump on Saturday said that Washington had identified 52 Iranian targets to respond "very fast and very hard" to in the event of reprisals from Iran over the killing.
The airstrike came after Iraqi protesters on December 31 stormed the US embassy compound in Baghdad to protest the American air raids conducted on December 29 against five bases of Iran-backed militias in Iraq and Syria, claiming the lives of 25 people.
( With inputs from IANS )