A leading security expert says there is no specific terrorist threat against Anzac Day or Easter mass services, despite police asking for fewer events to be held.

Auckland Council has scrapped 58 planned Anzac Day events at the urgings of police, who are keen to maintain a visible presence following last month's Christchurch mosque shootings in which 50 people were killed.

It means just 26 official Anzac commemoration events will be held in Auckland this year.

There are also reports a Wellington Catholic church has arranged security for its Easter mass services, although the Auckland Catholic Diocese says it will not be stepping up security, aside from remaining vigilant.

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Some have labelled moves to scrap Anzac Day services as "overkill" and giving in to terrorists, who want people to live in fear, while others say we need to be careful in case there is another attack.

Security analyst Paul Buchanan from 36th Parallel Assessments said the heavy emphasis on security since the Christchurch attacks was based on a "blueprint" commonly used in Europe in which countries go into a high risk, alert status for 4-6 weeks.

The idea was to show an "abundance of caution" because there was typically a higher risk of follow-up and revenge attacks immediately after terrorist events.

In New Zealand, this had led police to offer 24/7 protection to all mosque and Muslim community centres and that was yet to be wound back.

But despite the massive operation, there was no intelligence indicating an attack was imminent, Buchanan said.

Therefore, a police request to hold fewer Anzac Day events was about logistics.

"We simply don't have the man power at the moment to do security for all the original Anzac Day commemorations," he said.

"I happen to have friends who are police officers - they are zombies ... overworked and underpaid."

Buchanan said the outpouring of grief and support that Kiwis and the Government had shown to the Muslim community had helped lessen the threat of any revenge attack.

"We've done all the right things as a nation," he said.

"There are only about a couple of hotheads in the Muslim community in New Zealand. They are heavily monitored and the community leaders are stifling them."

While there was no intelligence suggesting an imminent attack, Buchanan believed right-wing extremism was a greater threat.

He said there were other people in the South Island, particularly, who may have been radicalised on the internet in a similar way to the Christchurch shooter, and who may have legally purchased powerful weapons like he did.

"They are still out there - so if I was to bet on a possible terrorist attack in the near future, it might be a follow-up attack from the right-wing extremists," he said.

But such an attack was less likely to target an Anzac parade or Easter mass service, he said.

A police spokeswoman said police would maintain a visible and "heightened presence and readiness, in line with the national threat level remaining high".

"This includes continued armed guards at events of significance," she said.

"Our advice to churches regarding Easter gatherings is the same for any type of large gathering/event while the threat level is high - remain vigilant and report anything suspicious."

Dame Lyndsay Freer, the spokeswoman for the Catholic Diocese of Auckland, said there were no plans to put security in place for Easter mass services, but that churches would remain vigilant.

The Anglican Diocese of Auckland said in a statement it was seeking guidance from police about security and any potential threats to churches.

"Our ministry units are being encouraged to proactively engage with the New Zealand Police in discussing security precautions," it said.