The military said there were three injured survivors so far from the crash, which happened when a C-130 Hercules aircraft was trying to land in Guelmim, having flown north from the disputed Western Sahara territory.
A resident in the area told Reuters there was thick fog in the area at the time of the crash, which occurred at 9am (0800 GMT) some 730 km (450 miles) south of Rabat.
"The crash, due to bad weather conditions, caused 78 deaths and (left) three seriously wounded," Morocco's Royal Armed Forces said in a statement carried on the official MAP news agency.
The military said that 60 soldiers, 12 civilians and nine crew members were on board at the time of the crash.
The three survivors and 42 bodies recovered so far have been taken to the nearby military hospital, the military said.
The MAP news agency said that the plane had been travelling from the Western Saharan city of Dakhla and was due to travel on to Kenitra, 40 km (25 miles) north of the capital, Rabat.
Morocco keeps the majority of its soldiers in Western Sahara, a territory about the size of Britain, that Rabat annexed in 1975.
Morocco's most recent plane crash was in 1994 when all 44 passengers and crew members aboard a Royal Air Maroc aircraft died in a crash near the southwestern city of Agadir.