Prime Minister Peter O'Neill -- who protesters were calling on to resign amid accusations of corruption -- blamed
"agitators responsible for instigating a violent confrontation."
Witnesses told CNN that students had gathered on the University of Port Moresby campus, and were intending to go to Parliament to protest when police blocked them from leaving.
"Police came into campus and stopped the students from going to parliament," he said.
"Police started swearing at the students, insulting them (and then) fired shots at them," Anjo said. "I was lucky to escape ... people ran for cover in all directions."
Anjo said "many students were injured," after police "fired continuous shots" into the crowd.
Commissioner of Police Gari Baki said around nine students were admitted to hospital and treated for injuries sustained "allegedly in a confrontation with police at the Waigani Campus."
Protesters have been calling for O'Neill to step down for several weeks, amid accusations of corruption within his office.
"This protest and the factors that led to the incident today have been driven by people who are not students," the Prime Minister said.
"This is now a law and order issue. We must obtain the facts and ensure this does not happen again in the future."
Local lawyer Hubert Namani told CNN there were "riots and protests starting up all over the city," in solidarity with the students. He added that he had closed his business and sent staff home due to the unrest.
"The students are getting all of the support now," he said, adding that he had heard sporadic gunfire from several parts of the city after the incident.
Anjo said protests would continue.
"Students and civil society will not stop unless and until the Prime Minister resigns from office or surrenders to police and is arrested and charged."
Australia's Department of Foreign Affairs and Trade issued guidance to citizens in PNG, warning there are "reports of looting and unrest in other parts of Port Moresby including Gerehu and the Hahola Markets. There are also reports of unrest related to student protest in other parts of the country.
In a statement, the U.S. Embassy in Port Moresby said the "situation is still volatile and could escalate at any time."
Australian Foreign Minister Julie Bishop called on all sides "to deescalate the tensions and ... respect the peaceful and lawful right to protest."
Human Rights Watch issued a statement calling on Prime Minister O'Neill to immediately launch "an impartial, thorough and transparent investigation."
"The police shooting of protesting students in Port Moresby is shocking, and a truly terrible incident," HRW's Deputy Asia Director Phil Robertson said.