One survivor has been found and the search continues, emergency services official Col Farid Nechad told public radio.
The plane is said to have been carrying military personnel and family members.
The survivor is a soldier who is now being treated for head injuries at a military hospital in Algiers, a retired Algerian intelligence official told Associated Press news agency, on condition of anonymity.
Women and children were among 77 bodies recovered from the crash site so far.
Dozens of rescue workers are said to have reached the scene, despite the mountainous terrain and wintry weather conditions.
President Abdelaziz Bouteflika sent his condolences to families of the victims and has decreed three days of national mourning to begin on Wednesday, said state TV.
‘Storm and snowfall’
The plane was carrying 99 passengers – soldiers and their families – as well as four crew members.
The plane’s original departure point was the Sahara Desert garrison city of Tamanrasset, 1,500km (950 miles) south of Constantine, but it had made a stop in Ouargla.
A source told radio station Ennahar – which has close links to the government and army – that contact was lost with the military plane between Oum al-Bouaghi and Constantine, as it may have been starting to make its descent prior to landing.
It crashed into Djebel Fertas mountain, some 380km (240 miles) east of the capital Algiers.
“Very bad weather conditions, involving a storm and heavy snowfall, were behind the crash,” the defence ministry was quoted as saying in a statement.
This is the worst plane crash in Algeria for more than 10 years and the third involving an Algerian military Hercules.
An Air Algerie Boeing 737 crashed on take-off from Tamanrasset in 2003, killing all but one of the 103 people on board.