The funeral processions began at Baghdad's al-Muthanna airport and headed to al-Kadhimiya, a sacred city for Shiite people, according to Popular Mobilization Forces, a Shiite Iraqi militia whose deputy leader Abu Mahdi al-Muhandis was also killed in Friday's strike, Efe news reported.
The coffins of al-Muhandis and other Iraqi members of the militia were covered by their country's flag, while Soleimani's was covered by the Iranian flag.
The bodies were moved from al-Kadhimiya to al-Jadriyah, also in Baghdad, by four-wheel-drive vehicles amid strengthened security measures, including the presence of armed militia, according to footage broadcast by the Iraqi state-run al-Iraquiya TV.
Iraqi Prime Minister Adel Abdel-Mahdi took part in the funeral proceedings, as did former prime minister Nuri al-Maliki and head of the Popular Mobilization Forces' Authority Faleh al Fayad.
Later on, the convoy would head to Karbala, a holy city for Shiite people, where top Shiite cleric Ali al-Sistani is based, and Najaf city, both of which are located 100 km to the south of Baghdad.
In Najaf, funeral prayers will be given and the Iraqi citizens will be buried. Soleimani's body will be returned to Iran.
Earlier in the day, Iran's President Hassan Rouhani warned the United States of consequences over Soleimani's killing.
"The Americans were not aware of the big mistake they made; they will face the consequences of their crime, not only today but also in the coming years," Rouhani said as he visited relatives of Soleimani, who was killed in a US drone strike outside Baghdad's airport on Friday.
Gen. Soleimani was in charge of Iran's foreign policy strategy as the head of the Quds Force, an elite wing of the Islamic Revolutionary Guard Corps, which the US has designated as a terror organization.
The Quds Force holds sway over a large number of Shia militias across the region ranging from Lebanon to Syria and Iraq.
The targeted strike took place amid increased tensions between Washington and Tehran after hundreds of protesters stormed the US Embassy in Baghdad on 31 December, where they managed to breach the main gate and enter some rooms, lighting fires.
On 27 December, more than 30 rockets were fired against the K1 military base in Kirkuk, in northern Iraq, killing an American contractor and wounding several US and Iraqi military personnel.
The Pentagon believes that the Shia militia group Kata'ib Hizbollah was responsible for attacks that since mid-October have targeted military bases and government facilities where US personnel are deployed to support the Iraqi army.
In response to the first fatality, the Pentagon carried out "defensive attacks" in Iraq and Syria against the KH, which killed at least 25 people, according to the PMF.
The action resulted in the assault on the US Embassy.
( With inputs from IANS )