"My view, as I have said to ... [Prof Todd] is I think they have got some good people working there, but they do need to focus on the development of their international business a bit more aggressively.
"As one of our top universities, it's important to the whole system that they continue to develop their international offering and their international linkages," he said.
The comments come after Prof Todd said in a report tabled at a university council meeting this week that Education New Zealand had been "slow" when it came to developing a "unified" brand for the country and plans for specific countries.
Mr Joyce took issue with these comments, saying this view was not "consistent" with what others in the sector were saying.
"They are doing it very well, they are doing it a heck of a lot better than the previous trust based-model was," he said.
Mr Joyce also had some questions over the level of influence the Christchurch earthquake was still having on international enrolments, with Prof Todd continuing to blame the quake for "depressed demand" from international students.
He noted that international student numbers were increasing at some other South Island institutions, including at Otago Polytechnic.
"I think it would be difficult to explain a decline in numbers because of the earthquakes," he said.
He accepted the high exchange rate was making things more difficult, but pointed out that other institutions were also dealing with the same issue.
The university was unable to respond to Mr Joyce's comments yesterday.