ICC prosecutors have charged Duterte with three counts of alleged involvement in crimes against humanity, involving at least 76 killings between 2013 and 2018 during Duterte's anti-drug campaign.
Prosecutors also said Duterte personally selected certain victims.
The 80-year-old Duterte denies the charges and refused to participate in Monday's hearings.
The Philippines left the ICC in 2019, but the court has the right to try crimes committed between 2011 and 2019. The ICC hearing will last four days, after which the judges have 60 days to decide whether the evidence is sufficient for a trial.
Correction: An earlier version contained an incorrect statement about Duterte's presence.
