Auckland University's vice-chancellor Stuart McCutcheon says if New Zealand does not want the country's best and brightest people studying offshore, it needs to provide top-quality tertiary education.
Tertiary Education Minister Steven Joyce said universities must target international students to increase their income.
Stuart McCutcheon said the debate about New Zealand's universities needed to focus on the quality first, and the cost second.
He said the country must address its universities' decline in international rankings.
"I think that our young people should have the opportunity to go to universities of genuine international quality because today's younger generation are very aware of the rankings of universities, very aware of the quality of the universities and what we don't want are our best and brightest going overseas to study."
The University of Auckland has asked the Government to remove the restrictions on charging higher fees to address the decline in international rankings.
Universities must not increase their fees by more than 4 percent each year.
Mr Joyce told Television New Zealand's Q+A that New Zealand universities needed to bring in more money from overseas students.
"If you're comparing them with say with New South Wales or Queensland, those universities each collect about $300 million a year from international income. Auckland collects about $90 million a year.
"If you look at that, you say, well, there's no way the Government is going to pony-up for the other $210 million a year.
"Auckland does have to get a bit more focused on international income."
Professor McCutcheon said the question of funding came after the decision of whether or not New Zealand's universities should be among the best in the world. He said high quality universities have a huge benefit to society.
The president of the Union of Students' Associations said the Government must boost funding to ensure the country has world-class tertiary education.
Daniel Haines said overseas students will only come here if the institutions are of high quality, but students cannot afford to pay any higher fees and enrolment is already falling at five of New Zealand's eight universities.