Students in Papua New Guinea marched to their university in the capital Port Moresby covered in mud as a sign of mourning after police last week shot at protesters.

PNG authorities had demanded students return to classes on Tuesday, and end a six-week boycott over demands for Prime Minister Peter O'Neill to stand aside and face a corruption investigation.

Anger boiled over on Wednesday after police confronted students outside the University of Papua New Guinea campus to prevent a march on parliament, opening fire and wounding at least a dozen students.

David Pepson, a law student, told Fairfax Media the campus was mostly quiet on and empty on Tuesday, with students not ready to go back to class.

He said the mud on faces was a Melanesian mourning custom.

International organisations, including Transparency International and Human Rights Watch, have called for an independent inquiry into the police shootings.

Prime Minister Malcolm Turnbull offered Australian help in the aftermath, but Mr O'Neill said it was an internal matter for PNG.

Mr O'Neill has been fending off a corruption investigation after police issued an arrest warrant in 2014 to question him about claims of millions of dollars in fraudulent payments to a local law firm.

The PNG budget has also been hit hard by the global downturn in commodity prices, forcing massive cuts to funding for education and health.

In a statement on Monday, Mr O'Neill said his government was committed to offering children an education.

"In any country it is never easy to find a job, but a good education can enable our children to have a good and successful in the future.

"I urge all parents to talk with their children on education importance and leave politics behind, as it will only do harm to them," he said.