The group is made up of NZ Security Intelligence Service (NZSIS), the Government Communications Security Bureau (GCSB), the Defence Force, Police, Corrections, Ministry of Foreign Affairs and the Civil Aviation Authority.
Medium is defined as when a terrorist attack is assessed as feasible and could well occur. The new level remains higher than it was before the March 15 terrorist attack, when the threat level was low.
Before the attack, New Zealand terror threat level had never been higher than "low".
Ardern said: "While the threat level has been revised to medium, and there is no current specific threat agencies are responding to, people will continue to notice a clear Police presence at public events, including on Anzac Day.
"Government organisations, including Police, are required to assess their own security settings and ensure they are appropriate when there's a change to the National Terrorism Threat Level and they will make operational decisions accordingly."
Ardern said that behind the scenes there remains an extensive cross-agency response to counter any potential threats.
"A number of agencies, including the Police and NZSIS, continue to work hard to understand, mitigate and manage threats and I am receiving regular briefings on that work."
She said New Zealanders should go about their daily lives as normal, but remain vigilant.If you see something suspicious or behaviour that concerns you, Ardern asked that people "speak up and call the Police".
"I'm very heartened that people have been doing this since the Christchurch attack, while also continuing to show their support and solidarity with the Muslim community across the country."
CTAG was set up in 2004 in response to changes in the global terrorism environment post September 11, 2001, and the Bail terror attacks in 2002.
CTAG has a six-tiered threat-level system starting at negligible – where a terrorist attack, violent protest activity or violent criminal behavior is assessed to be "very unlikely".
It goes all the way up to extreme, which is assessed as when a terrorist attack, violent protest activity or violent criminal behavior is expected imminently.
CTAG is tasked with setting the threat level, and it does so independently.
But how New Zealand responds to that threat level is determined by the senior officials' advisory group for emergency situations – ODESC.
It considers the appropriate response and then makes recommendations to senior ministers, including the Prime Minister.
But each agency within CTAG is responsible for responding to the threat level. For example, the police have decided to station armed officers across the country.