Victoria University is blaming the Tertiary Education Union for blocking its attempts to pay union staff more money.
The union had said the job ad was a breach of good faith and has asked the university to take it down.
But the university's vice-chancellor, Grant Guildford, said it was the union that was at fault - union members had been offered the same pay rates as non-union staff, but the Tertiary Education Union had turned them down.
"It's a deeply mysterious situation to us," he said.
"For some reason they're refusing to accept that on behalf of the union staff."
The university's offer included modern terms and conditions of employment, Professor Guildford said.
"We're puzzled... the university's been attempting to move to a remuneration process that's similar to all the other universities in the country whereby the salary ranges are market informed.
"Because our staff were getting further and further behind the pay rates of equivalent roles in the city here, we felt it was very important that we went on and at least attended to that [for] the non-union staff so they weren't being held at a disadvantage by a union to which they didn't belong."
But the Tertiary Education Union's deputy secretary, Nanette Cormack, said the university offer had come with conditions, including reserving the right to determine future pay rates for about 400 non-academic staff.
"We think the whole purpose of collective bargaining is to discuss all of the terms and conditions of employment which have got to include salaries, and that's what our members are very strongly saying, that they expect their employer [the university] to talk to us about," she said.
Mr Guildford denied the comments, and said the union would not be excluded from future pay negotiations for those staff.
"There's no facility for the union to be shut out of the bargaining in a collective contract's future pay rates," Professor Guildford said.
"The bargaining team have made very clear, abundantly clear, over the last month that that was not the situation."