The second boat carried 69 illegal migrants, including two Egyptians and dozens of Sudanese, the Red Crescent added without specifying their fate.
Khums is a coastal city, some 118 kilometres east of the capital, Tripoli.
On Wednesday, the International Organisation for Migration said that at least 42 illegal migrants went missing and presumed dead after a rubber boat sank near the Al Buri oilfield, an offshore facility north-northwest of the Libyan coast.
