At a Khartoum news conference Sunday, Interior Minister Zubair Bashir Taha said it was an "embarrassing matter," Ynetnews reported Monday.
"Has Egypt become the gateway to Israel or to Europe? We don't know where these people are headed ... they know nothing about Israel," he said.
Taha said Egyptian authorities were assisting the investigation, as many of the refugees were spending prolonged periods in Egypt before going to Israel.
Israeli Prime Minister Ehud Olmert's office issued a statement saying refugees who weren't from the war-torn Darfur region would be returned to Egypt, the report said.
2014: The Year in Music [PHOTOS]