The call comes amid an upsurge of attacks on civilians and UN peacekeepers, as well as renewed fighting between factions.
Prosecutor Fatou Bensouda's call comes amid an upsurge of attacks on civilians and UN peacekeepers, as well as renewed fighting between factions of the Christian anti-Balaka coalition and the mainly Muslim ex-Seleka rebels.
"Violence and clashes between armed groups in several parts of the Central African Republic (CAR) have increased in the last months," Bensouda said in a statement.
"These reported crimes may fall under the jurisdiction of the International Criminal Court and must immediately stop," she said from the ICC's Hague-based headquarters.
A UN official said fighters used mortars and grenade launchers 10 days previously in an assault in Bangassou near the border with the Democratic Republic of Congo. The southeast town had until then mainly been spared from violence.
The offensive left at least 115 people dead including a Moroccan peacekeeper.
Five other peacekeepers -- four Cambodians and a Moroccan -- died on May 8 when their convoy was ambushed not far from Bangassou, in the deadliest attack so far on the UN mission.
Fighting erupted in two other towns -- Alindao and Bria -- that have left scores dead but those clashes were among factions of the anti-Balaka coalition and ex-Seleka rebels, officials say.
In Bangassou, the attack blamed on anti-Balaka rebels targeted the UN's MINUSCA base before turning onto Muslims.
Control of resources in the area -- which is rich in diamonds, gold, coffee and cattle trading - may have played a role in fighting, deputy UN envoy Diane Corner said last week.
Hundreds of reinforcements were sent to Bangassou to restore calm, and Corner said the situation remained "extremely fragile."
The United Nations has 10,000 troops and 2,000 people serving in its MINUSCA force in Central African Republic, which descended into bloody sectarian fighting after the 2013 overthrow of leader Francois Bozize.
Bozize, a Christian, was ousted in March 2013 by mainly Muslim Seleka rebels, triggering the worst crisis since independence from France in 1960.
The ICC, which was already probing crimes committed by former DRC vice president Jean-Pierre Bemba's forces in the CAR, in 2014 opened a second investigation into an "endless" list of atrocities committed by armed militias since August 2012.