President Jacob Zuma has urged protesting students to return to class, saying there will be consequences for those who act criminally.

"Government is committed to do everything possible to progressively make higher education more affordable and free for the poor. I would want to make a call to let the students go back to study," Zuma said at a higher education summit on Monday.

Zuma added that he had instructed law enforcement agencies to arrest criminal elements who were hijacking student protests.

He condemned violence and the destruction of property, saying the resolution taken last year not to increase fees was made through strategic dialogue.

He said the 8% cap on university fee increases announced by Higher Education Minister Blade Nzimande also came about through strategic dialogue with stakeholders.

"The 0% fee increase for 2016 was a decision made through listening and talking. The summit is doing what South Africa does best - to meet and talk and find solutions. Together we find lasting solutions," he said.

Zuma said an inquiry into higher education must be given a chance to find a way out of the impasse over fees.

"Work is being done to find solutions," he said.