The Tertiary Education Union (TEU) has lowered the pay rise it is seeking for university staff from 8 percent to 7.2 percent.
TEU national secretary Sandra Grey said the change matched the most recent estimate of the annual rate of inflation.
"We still think that those working in education deserve a pay rise that actually helps them cope with the rising cost of living," she said.
"You can't pay people under the cost of living increase."
Grey said members at Victoria, Canterbury and Otago would meet this week to discuss improved offers but the union remained a long way apart from the remaining five universities.
"Some of them have not even moved their offer at all and this is really, really concerning because we've been asking them to come to the table with a real deal for months now," she said.
Members of the TEU and other unions have taken industrial action at the universities since a national day of strikes and rallies in early October.
This week union members at the University of Auckland were withholding students' marks while those at the University of Waikato called off similar action on Monday after the university said it would suspend any staff who participated.
The University of Auckland previously told RNZ it had offered staff a 9 percent pay rise over two years and 11 percent for staff paid $60,000 or less.
AUT told RNZ it was offering staff a 2.75 percent pay increase.
The University of Waikato said its previous offer was 2 percent with some additional payments but talks were continuing.
Otago, Lincoln and Victoria would not comment as they were either already bargaining or about to resume bargaining.