He said the bank would be monitoring progress and would not hesitate to act if management of online content did not meet the standards expected by ANZ, its customers and the public.
A Westpac New Zealand spokesman said its advertising on Facebook remained suspended.
"We took this step so we could engage with Facebook to understand its level of commitment to reducing the publication of harmful content."
The bank said it acknowledged Facebook had since made a number of public commitments.
In an open letter published in the Herald on March 30 Facebook chief operating officer Sheryl Sandberg said it would be strengthening the rules for using Facebook Live and taking further steps to address hate on its platforms.
"We are exploring restrictions on who can go Live depending on factors such as prior community standard violations.
"We are also investing in research to build better technology to quickly identify edited versions of violent videos and images and prevent people from re-sharing these versions."
Westpac said it was now working through how those measures would be implemented in practice and whether advertising, or leveraging its position as an investor was the most effective way it could continue to apply pressure on Facebook.
The bank is one of 18 fund managers who have joined the New Zealand Superannuation Fund and other government-backed investors to try and pressure the social media player to make changes.
A BNZ spokesman said it was not working to a timeframe on advertising and would be monitoring the intention of the social media platforms in the coming weeks and months.
"We support what the World Federation of Advertisers has called for – more controls on livestream functionality – and we agree with the Prime Minister, they aren't just the postman and that comes with a level of responsibility.
"We're watching with interest to see how both platforms respond to the new laws in Australia, as New Zealand is often included in responses or product changes that happen there."
A spokeswoman for ASB said it was in discussions with the wider industry and Facebook to ensure tighter controls are introduced for livestreaming.
"We are pleased Facebook has indicated it will make changes to the eligibility criteria for livestreaming, and are awaiting further details before deciding whether to return to paid advertising on the platform."
But Justine St John, TSB general manager marketing and customer experience, said while Facebook had signalled they were going to take steps to control harmful live streaming being posted and shared "we are yet to see any action from this".
"As no changes have actually been implemented TSB is still continuing to suspend all Facebook advertising."
A spokeswoman for Kiwibank said it was continuing to review the situation on a regular basis.
While the New Zealand banks put advertising on hold their Australian parents have continued to advertise on Facebook.
Asked why the banks were sending a different message in Australia to New Zealand the New Zealand arms said it was because they were managed independently.
"ASB has its own board and management and operates independently from the Commonwealth Bank of Australia," a spokeswoman for the bank said.
BNZ said while it had made its decision independently of its parent National Australia Bank "we know they have been following the matter closely."
The Westpac spokesman said: "Westpac NZ is managed independently of Westpac Banking Corporation and makes its own decisions around marketing and advertising."
