ICTR spokesperson Roland Amoussouga told Hirondelle News Agency that the former lawyer suffered from the effects of "previous medical problems".
He said that according to the police preliminary report and medical investigations, it was revealed that the death could be the result of natural causes.
However he said "We are awaiting for the complementary results of the toxicological test and other examinations to determine with more precision the exact cause of his death."
He ruled out so far the possibility of assault.
"It should be noted that the preliminary reports exclude the assumption of any violence on the body which can suggest murder", underlined the Tribunal Spokesperson.
Last week, the Tanzanian police had announced the opening of an investigation into the circumstances of the death of the young Sri Lankan attorney.
According to the police commander in Arusha, Basilio Matei, Rajapaksa's body was found on ground in his residence on 12 August, bleeding from the mouth and nose.
The first person to have discovered the body was the housemaid who immediately alerted the police.
© Hirondelle News Agency