"We need to put a deadline on this because schools are about to begin working out end-of-year payments and it seems that the problems are compounding."
Mr Goulter said the problems plaguing Novopay had caused stress to schools and staff.
"Now the latest security issues around teachers' pay details are further indications that there are ongoing and serious system problems.
"Clearly the $30 million pay system was not ready and properly tested before it was introduced and the Ministry of Education can no longer continue to downplay these problems."
Prime Minister John Key today said it was essential to bring in the Novopay system because the previous system was "effectively falling over".
"Novopay was late, so that made the situation even worse and then there are about three different layers that teachers can be paid at.
"So a lot of the basic stuff, as I understand it - I could be wrong - but as I understand it, is happening just fine," he said on TVNZ's Breakfast show
But he said it was not acceptable that there had been so many errors with the system.
"I think the vendor here, Talent 2, they are responsible for the system and we contract them like any other company and the pressure has to come on them."
Mr Key said if the problems were not fixed, it would probably face a financial penalty.
Novopay business manager Rebecca Elvy said the payroll failings were being addressed.
"We've developed a way for relief teachers to follow up their pay issues without needing to go through the various schools they work for. We've made substantial fixes to the reports schools use to verify their payroll - and we're continuing to work towards a 100 per cent fix on that issue," Ms Elvy said.