The independent regulator of Australia's universities has been asked to investigate the widespread cheating among international students exposed this week.

Fairfax Media revealed on Wednesday up to 1000 students had used a Sydney-based company called MyMaster to buy their university essays for up to $1000.

The federal education department told a parliamentary hearing on Friday the issue had been referred to the Tertiary Education Quality and Standards Agency (TEQSA), which is responsible for assuring the quality of Australia's universities.

Jessie Borthwick, deputy secretary for higher education, research and international at the Department on Education, said Fairfax Media's revelations were very concerning because "they go to the issue of Australia's international reputation".

"We would expect universities equally to take these allegations very seriously and to institute their own internal processes of review into these matters," she said.

"We'll have further conversations with TEQSA next week and we'll decide at that point what action needs to be taken."

The department's secretary, Lisa Paul, said universities cared deeply about their reputations and "we would expect universities to take strong action if there is any cheating of any sort".

It adds to mounting pressure for the universities to launch internal investigations into the cheating. Students from 16 Australian universities used the MyMaster website this year to pay for assignments and have online tests completed.

Labor's higher education spokesman Kim Carr said on Thursday the federal government had a responsibility to protect Australia's international reputation for education.

As of Friday afternoon, only one university, Wollongong, had indicated it would investigate.

"We are concerned and disappointed of media reports suggesting a small number of UOW students have allegedly paid for an essay or assignment writing service and have requested further information and will look into the alleged offences," the university's deputy vice-chancellor, Professor Eeva Leinonen, said in a statement on Wednesday.

Fairfax Media will provide the universities with information that will assist in their investigations, including copies of completed assignments that they will be able to cross reference.