King, seeded sixth in the tournament, dropped just one game in a 6-0, 6-1 win over Mouhtassine in the clay-court tournament.
The only other seeded player to draw a Monday match was No. 9 Jarmila Gajdosova, who was a 6-3, 4-6, 6-1 winner other Melinda Czink. Also Monday, Alize Cornet defeated Nuria Llagostera Vives 7-5, 6-1.
Sania Mirza is the top seed for the Moroccan Grand Prix, where the champion will earn $21,140.
Celebrity Families of 2014 [PHOTOS]