Rescue teams reached the wreckage more than four hours after the ATP turboprop plane crashed on Sao Jorge island, scattering debris and bodies across a densely forested ravine.
The airline said it would reveal the identities of the 31 passengers and four crew only after their families had been contacted.
Seven bodies were recovered as rescuers using ropes and carrying stretchers scrambled over the steep, rugged mountainside, combing the area before night fell.
Jose Joaquim, a rescue official, told TSF radio it was unlikely survivors would be found.
Thick mist shrouded the area, which was inaccessible to vehicles, TSF reported.
Portuguese Air Force helicopters were on standby to winch out any survivors.
The Azores, a nine-island group, lie about 900 miles west of mainland Portugal.
Sao Jorge is 35 miles long and five miles wide and is sparsely inhabited. The mountain range where the plane came down has steep escarpments rising more than 3,300 feet. There are few paved roads in the crash area.
"It's a very difficult area to work in," Dionisio Silveira, head of the local Civil Protection Service, told state radio Antena 1.
The 64-seat aircraft was on a local inter-island flight when it crashed in thick fog.
The plane left Ponta Delgada on Sao Miguel island at 8:37 a.m. en route to Horta, on the island of Faial, about 190 miles to the west, Antena 1 reported.
At 9:13 a.m. the captain told air traffic controllers he was beginning his descent to Horta. The last contact was at 9:19 a.m., Antena 1 said.
No emergency call was received from the aircraft before it went down. The cause of the crash was not immediately known, though the pilot apparently had taken an alternative course to avoid bad weather on his planned route.
The pilot had more than 20 years' experience as a civil aviation pilot and his copilot was a former Portuguese Air Force officer, TSF radio said.
The aircraft, built by British Aerospace, had been in service between the islands for 15 years, according to Lusa.
All SATA flights were canceled after the crash. SATA is the only airline that flies between the islands.
Portuguese Prime Minister Antonio Guterres, who was in Helsinki, Finland for a European Union summit, canceled a planned visit to Kosovo and headed straight for the Azores Islands.
Emigration from the Azores to the United States is common and SATA has offered to arrange flights back to the islands for far flung relatives of crash victims.