The MP is making a statement to radiogagana.com website about the 2006 killings of Manoharan Rajikar, Hemachandran Yogaraja, Lohitharaja Rohan, Thangaturai Sivananda and Shanmugalaraja Gajendran, all aged 20 years of age.
Thurairatnasingham said families of the murdered students had to flee the country due to threats they had received.
He noted the then government rejected the blame for the killings and said they had been accused of being LTTE members.
The government had claimed they died in a bomb blast as they tried to attack the armed forces, said the MP.
No progress has so far been made in investigations into their deaths, despite inquest reports confirming that they had been shot, at close range.
Twelve STF men, including an ASP, were arrested on suspicion on 05 June 2013, but were given bail within four months, said the MP.
The UNCAT that met in Geneva recently expressed concern over the lack of progress in the investigation and urged the government to ensure justice for the students.
According to a wikileaks revelation, the then minister Basil Rajapaksa had admitted to US ambassador at the time Robert Blake that the government knew the STF was responsible, but that no action could be taken due to a lack of adequate evidence.