Parliament in Baghdad also called for a ban on foreign forces using Iraqi land, airspace or water for any reason.
The US has some 5,000 military personnel in Iraq, mainly as advisers.
Thousands of Iraqis attended a funeral procession for Soleimani before his body was flown to Iran.
Iraq finds itself in a difficult position as an ally both of neighbouring Iran and of the US. Thousands of US troops remain in the country to assist in the broader struggle against the Sunni Muslim Islamic State (IS).
But the government sees the killing as a violation of its sovereignty, and of the terms of the coalition presence in Iraq.
Meanwhile, a variety of Shia militia groups in Iraq are supported by Iran, and there are concerns that parts of Iraq’s population sympathetic to Iran have been alienated by the killing, and that militant groups may seek revenge.
Iraq’s parliament met as hundreds of thousands of people turned out in Iran to mourn Soleimani.
The non-binding resolution was passed by the Iraqi parliament on Sunday after the caretaker Prime Minister, Adel Abdul Mahdi, called for an end to the foreign military presence in a speech to MPs.
Calls for revenge have multiplied in Iran since Soleimani’s assassination, which has thrown US foreign policy in the Middle East into question.