According to almaalomah.com website, the bodies are planned to be transported to the holy city of Najaf later.
They were killed in a strike by American drones near Baghdad International Airport in the early hours of Friday.
The White House and the Pentagon confirmed the assassination of General Soleimani in Iraq, saying the attack was carried out at the direction of US President Donald Trump.
Their funeral service began in the Iraqi capital on Saturday morning.
The procession continued at the Kadhimiya shrine north of Baghdad as mourners marched in the streets in a solemn procession.