Police arrest Mitchell Shane Moulton in Ferry Rd, Christchurch, after it is alleged he threatened Work and Income staff.

Two police officers who chased a man they believed had a gun insist they are no heroes.

Constable Chris Buckley and fellow constable Liam Platt-Young were doing routine traffic patrolling on Bealey Ave when the call came through that a man had allegedly threatened staff at a Work and Income office.

Police say the offender tried to get inside the locked Linwood office about 8.45am, and threatened office workers and security staff before leaving in his car.

The pair "armed up" on their way to the scene.

"Whilst we were heading into the area we saw a guy walking on foot who we had a second look at and thought might possibly be the informant, but he saw us, didn't acknowledge us and kept on walking."

They kept on driving until Platt-Young showed Buckley a photo of the alleged offender that had been sent out to police.

"We saw the photo and kind of looked at each other and thought we need to go back and check on that guy who we have seen on the street," Buckley said.

"We pulled over and spoke to him and I guess he didn't realise that it was us that had seen him walking on the road and he denied being there."

The man eventually arrested, Mitchell Shane Moulton, 32, then "did a runner" from the pair.

They went in pursuit of Moulton, Buckley carrying a pistol and a Taser and Platt-Young a rifle.

"Any other police officer working today would have done the same thing," Buckley said.

Moulton stumbled and fell on the road, Buckley said.

A photograph of the arrest had been posted to Facebook, with both officers getting plenty of comments from their colleagues.

Buckley had been labelled "buns of steel", while Platt-Young was already preparing to shout his workmates.

Moulton has been charged with being in possession of a pistol, discharging a firearm in Aldwins Rd and possession of a cannabis plant.

In the Christchurch District Court, Judge Bridget Macintosh remanded Moulton in custody, for a legal aid application, to an video link from the Christchurch Men's Prison on October 19.

Inspector Derek Erasmus said the incident was a "great example" of police doing a "fantastic job".

"Any of the cops would have done that but it wasn't any cop it was these two who were faced with the situation and they reacted in a way that the police and the public of Christchurch should be proud of."

Canterbury Police District Commander Superintendent John Price said no-one was injured.

All Work and Income offices in the city were placed in lockdown as a precaution but later reopened.

"Everyone has a right to be safe and feel safe whether at home or at work. This behaviour will not be tolerated and the prompt action of Winz staff alerting police ultimately led to the [offender] being located and arrested," Price said.

Police officers would visit Canterbury Work and Income offices to reassure and support staff, Price said.

Ministry of Social Development chief executive Brendan Boyle said threats to staff were taken "very seriously".

"People cannot and should not be able to threaten others without consequence," he said.

In September 2014, Ashburton women Peg Noble and Susan Leigh Cleveland were shot dead in the Cass St Work and Income office where they worked.

Russell John Tully, 48, was charged with their murders. He is yet to stand trial.