The students say police fired shots directly into the crowd. There are reports dozens of people were wounded.
Amnesty International, meanwhile, says the "disgraceful attack on the rights of peaceful assembly and expression" must be immediately investigated.
The organisation had received information that 38 people were injured, including four in critical condition, while three were still being assessed in the hospital's emergency department.
It also says witnesses have come forward claiming to have seen students beaten and shot at, including one student who was shot in the head.
"The shooting of students peacefully protesting is reminiscent of the worst excesses of repressive regimes in the region," said Rafendi Djamin, Director for South East Asia and the Pacific.
"Papua New Guinea's authorities must establish a prompt, impartial and independent investigation to determine who is responsible for the unnecessary and excessive use of force."
The prime minister has blamed the violence on the students and says police only fired tear gas and warnings shots.
Amnesty has condemned this response.
"Prime minister O'Neill's reaction has been completely inadequate. He should ensure an investigation worthy of its name takes place into reports of excessive use of force. Instead, he has prejudged the outcome, blamed the students for what happened to them, and sought to evade accountability," Mr Djamin said.
The prime minister has said an investigation will take place, although it's not clear who will undertake it or when it will happen. Mr Djamin said this wasn't good enough.
