Ardern indicated she had the support of Deputy Prime Minister Winston Peters for the changes, despite previous strong opposition from New Zealand First on the issue of tighter gun control.
The PM told reporters yesterday they will be discussing the more detailed policy at Cabinet today.
She said security agencies would also update Cabinet ministers today and those agencies would also be discussed.
"We need to make sure that we are looking more broadly at the work of our agencies, not just our intelligence services, police and our borders to ensure that we've taken a comprehensive approach and done everything we can to prevent any kind of action like this in the future."
She said there needed to be a "comprehensive response" to an range of issues the attacks had raised.
Opposition leader Simon Bridges said the National Party would back gun law reform.
"We will be ready and prepared to be constructive and to look at anything here because we do need to see some change," he said.