Khan says he now wants to open the investigation envisaged by his predecessor and broaden it to include crimes committed in fighting since the Russian invasion of Ukraine last week.
Khan said he would continue to monitor developments in Ukraine, where there have been reports of civilian casualties, and he called for "restraint and strict adherence to the applicable rules of international humanitarian law."
UN human rights chief Michelle Bachelet says her office has confirmed that 102 civilians, including seven children, have been killed in the Russian invasion and 304 others wounded in Ukraine since Thursday. She cautioned that the tally was likely a vast undercount.
Neither Russia nor Ukraine is among the court's 123 member states, but Ukraine has accepted the court's jurisdiction, which empowers Khan to investigate.
Khan has told his team to explore how to preserve evidence of crimes and said that the next step is to seek authorization from the court's judges to open an investigation. However, he added that the process would be speeded up if a member nation of the court were to ask for an investigation in what is known as a referral.
That "would allow us to actively and immediately proceed with the (prosecution) Office's independent and objective investigations," Khan said.
He said he also would seek support from the court's member states and the international community to fund the investigation.
"I will be calling for additional budgetary support, for voluntary contributions to support all our situations, and for the loan of gratis personnel," he said. "The importance and urgency of our mission is too serious to be held hostage to lack of means."