There was one survivor from the crash, according to the Hungarian interior ministry, who is in a critical condition in a Slovakian hospital.
The cause of the crash is not yet clear.
The death toll was revised down from 44 after Hungarian authorities received the official passenger list.
Those killed include seven crew members.
Hungarian interior ministry spokesman Tibor Dobson said body parts are scattered across the crash site.
"It is very grim," he said.
Mr Dobson said the AN-24 military plane was carrying Slovak peacekeeping troops from a mission in the UN-administered Serbian province of Kosovo when in crashed and burst into flames near Telkibanya, close to the Slovakian-Hungarian border.
"It's minus 18 degrees Celsius here. The plane's fuselage is completely burnt out. It is absolutely inconceivable that there could be other survivors," from the one already known, police spokesman Laszlo Garamvolgyi said.
Slovakia convened an emergency cabinet meeting after learning of the crash, and placed the Slovak army chief of staff in charge of a crisis unit.
"I imagine what the wives, the children, the fathers of the soldiers who were serving their country, are feeling," said a Slovakian Prime Minister Mikulas Dzurinda after the meeting.
The wife of one of the soldiers on board told a local TV channel that her husband contacted her to tell her of the crash.
"He told me that he was alive and to alert the rescue services and police. Then the line went dead," she said.
Difficult terrain has slowed the search and rescue effort.
Slovakia has some 100 troops stationed in Kosovo as part of the Nato-led peacekeeping force.