The man, who calls himself 'John Smith', told Norway's NRK channel that he woke up with a three-day beard in hospital on December 15th, with cuts on his wrist as if they had been strapped.
"The cuts were deep and it took several months before the wounds healed," he said. "It was quite obvious that my hands had been tied together."
A passerby found him in a snowdrift, and called an ambulance. He says that he had probably been drugged.
"I was paralyzed and could not speak. But the doctor said it was different drugs in the system," he said.
He then spent over twenty hours in a coma.
"I'm desperate, scared and want nothing more than to get out of this situation," he added. "I think I'm Czech, it is the language I understand best," he says. "I also understand Polish, Slovak and Russian. But I think and dream in English.
As far as he knows, he has no connection to Norway.
"I do not understand Norwegian, and I know no one here."
Smith has lived in Oslo for almost four months, after being discovered "in a bad condition" in a snowdrift in the east of Oslo on December 14th.
He has no idea of his name or even what country he is from. Police on Tuesday released his photo in the hope that someone would recognize him.
"At least I know I can't be a criminal, although I almost wish I was," he told NRK. "Then they would have found out who I was."
"I woke up with a nurse beside me, and as I did not understand, I asked her to speak to me in English. I remembered nothing. It was so funny when she asked what my name was and then I couldn't remember it."
Norwegian police said on Wednesday they had "interesting leads".
"We have received information from Norway but also from other countries and we find some of that information very interesting," Oslo police spokesman Sturla Henriksbø told AFP.
"It's particularly from the Czech Republic that we have received information," Henriksbø said.
Henriksbø, who works for the violent and sexual crimes unit at the Norwegian police force, confirmed that the man had marks and injuries on his body.