In a first of its kind ruling, the U.N. Security Council last week referred suspects accused of war crimes in Darfur to the ICC in The Hague. Egypt has said it does not want to see the "internationalisation" of Sudan's Darfur conflict.
"The International Criminal Court ... issues accusations but if the internal judiciary in the country concerned plays its role then it negates the need for the criminal court," Aboul Gheit said after meeting his Sudanese counterpart in Cairo.
"If there appears to be any reluctance (to prosecute), manoeuvring or attempt to dodge these accusations then in this case the International Court will make a move against the accused," Aboul Gheit added.
Khartoum has said it would refuse to hand over its citizens to face justice abroad. It says it has already arrested 15 members of the military and security forces for crimes including rape, killing civilians and burning villages in Darfur.
Rebels who launched a revolt in Sudan's vast western region in early 2003 say they welcome the decision to refer the suspects to the ICC.
U.N. Security Council Resolution 1593 does not specify whether Sudan can try the war crimes suspects itself.
Egypt has called a five-way summit of African leaders in Sharm el-Sheikh between April 18-19 to give the African Union a chance to deal with the crisis.