A resolution, overwhelmingly supported by the assembly, linked Yanukovych, who was ousted on Saturday and is now on the run, to police violence against protesters which it said had led to the deaths of more than 100 citizens from Ukraine and other states.
The resolution said former interior minister Vitaly Zakharchenko and former prosecutor-general Viktor Pshonka, who are also being sought by the authorities, should also be sent for trial at the ICC, which is based in The Hague.
But the war crimes court in The Hague says Ukraine has not yet asked it to investigate Yanukovych and others.