"The government must set a clear deadline for when all KiwiSaver funds should dump their investments in companies involved in the manufacture of these horrific weapons," said Green Party co-leader James Shaw.
But Jacqui Dean, minister for commerce and consumer affairs, said it was up to providers to act as soon as possible.
"When the issue of indirect investment in munitions was raised late last year, KiwiSaver providers undertook to divest those investments.
"I expect providers to do what they said they would do and exit from these investments as quickly as possible."
Asked what action the government would take if providers did not exit the investments Dean said she expected providers to listen to the concerns of consumers.
"As shown last year, public concern and consumer power forced the providers to respond to their concerns. I expect the providers to listen to the concerns of their consumers."
Sam Stubbs, the boss of new KiwiSaver provider Simplicity, said the funds should have their default status suspended.
Stubbs said the four KiwiSaver providers had enough time to transfer out of the investments and now they should be punished for not doing so.
"They clearly feel they can take their time. They need to receive the message that this is not trivial."
But there is no sign the government will take this option.
Dean said if providers had breached the law it was a matter for law enforcement agencies and investment choices that were lawful were a matter for the providers.
"However people always have a choice about which provider to be with and have the option to be with KiwiSaver fund providers who they are comfortable with."
An ANZ spokeswoman confirmed that its default fund still had some passive holdings in weapons makers via a passive index tracking fund.
But these would be transitioned to a fund managed by the ANZ shortly to ensure it had the flexibility to make further changes that investors might want.
"We will be confirming details in the next few weeks of a new investment solution which will ensure there is also no indirect investment in these kinds of companies for members of our ANZ Default KiwiSaver Conservative Fund."
She said the ANZ believed it was important to take the time to develop a future-proofed solution as it recognised that investor views on ethical investment would continue to evolve.
The bank wanted to ensure it could continue to deliver the best possible investment performance for its members while changes were made.
Kiwi Wealth chief investment officer Simon O'Grady said it had consulted with members on what they wanted and then had to go through an evaluation process to decide what it would replace its current offering with.
He said it had elected not to go with Vanguard's new ethical fund because it used an Australian unit trust which came with a significant tax drag for investors as well as a higher fee.
"Clearly to double fees and put a tax impost on investors is not the right outcome. So we decided to build our own."
O'Grady said it was on track to deliver that solution in the second quarter of this year.
He believed the process had not taken that long and said it was important for the firm to weigh up the economic impact any decisions it made would have on investors against the benefits.
A Westpac spokeswoman confirmed it would exit its investments by the end of the year.
RNZ reported that Mercer was still reviewing its investments.