Protesters started to gather in central Baghdad early on Friday, and several hours later, the area was packed with people.
Many carried Iraq’s national flags as well as placards denouncing the US military presence in Iraq.
The demonstration threatens to eclipse a separate protest movement involving mainly young people who for several months have been demanding a complete overhaul of the Iraqi government, says the BBC’s Martin Patience in Baghdad.
Some 5,000 US soldiers are in Iraq as part of the international coalition against the Islamic State (IS) group.
The two airbases targeted by Iran are in Irbil and al-Asad, west of Baghdad.
How did we get here?
The assassination of Gen Soleimani – head of the Revolutionary Guards’ elite Quds Force and architect of Iran’s policy in the region – was a major escalation in already deteriorating relations between Iran and the US.
The general was regarded as a terrorist by the US government, which says he was responsible for the deaths of hundreds of American troops and was plotting “imminent” attacks.
He was assassinated following an attack on the US embassy in Baghdad. Protesters were furious over the deaths of militia members in earlier US air strikes.
Washington blamed Iran for the embassy attack, with US President Donald Trump warning that Iran would “pay a very big price” for any damage or loss of life.