New Zealand police said Tuesday they were investigating a threat made this week against one of the Christchurch mosques where 51 Muslim worshippers were killed in a mass shooting a year ago.

Amid plans to mark the one-year anniversary of the March 15 massacre, police said the threat to Christchurch's Al Noor mosque was posted this week on encrypted messaging app Telegram.

Reports said the message showed a man in a balaclava sitting in a car outside the mosque accompanied by threatening text and a gun emoji.

"We have strong leads that we're following up and I'm confident that we will establish who this person is," Canterbury police commander superintendent John Price told Radio New Zealand, adding, "We're very close". 

Al Noor was one of two mosques targeted by a self-avowed white supremacist last year in what Prime Minister Jacinda Ardern described as "an unprecedented act of terror (that) shattered our small country".

The timing of the latest threat comes at a sensitive time as planning is underway for a memorial service in Christchurch to mark the anniversary.

Details of the service at the city's Hagley Park have not yet been finalised but Ardern is set to attend after gaining international praise for her compassionate handling of the attacks.

Ardern said Tuesday that she found it hard to believe that New Zealand's Muslim community was still being subjected to such hatred.

"I will be amongst many New Zealanders who will be devastated to see that as we head towards the one-year anniversary of a most horrific terror attack on the Muslim community, that they should then be the target of this kind of activity," she told reporters.

Price said he was encouraged that a member of the public had reported the threat, saying that people were acting to stamp out such online activity when they saw it.

"That's the way we'll conquer this issue in our society, is by everyone standing up and saying this is not OK," he said.

The alleged mosque attacker Brenton Tarrant, an Australian national, is due to go on trial on June 2 facing terrorism charges plus 51 counts of murder and 40 of attempted murder over the killings.