Australia will send response teams to New Zealand after its call for help responding to Cyclone Gabrielle, its worst storm in decades.

New Zealand declared a national state of emergency on Tuesday to the mammoth storm and is still coming to grips with the scale of the disaster.

More than 10,000 people have been displaced, with the worst hit regions in the country’s eastern Hawke’s Bay and Tairawhiti regions.

Five Australian impact assessment teams, totalling 25 people, will travel to New Zealand this week to help with the National Emergency Management Agency (NEMA) with rescues and recovery.

“NEMA has accepted an agency-to-agency offer from Australia for emergency response support and expertise,” Prime Minister Chris Hipkins said.

“They’ll be looking for people if the people are missing.

“They’ll be looking at buildings, whether they are habitable or not and providing that intel back … about what areas need to stay evacuated.”

The death toll has risen to six and could continue to grow as rescue and recovery efforts from the massive storm continue.

A man in his 60s was killed in floodwaters in the Gisborne region overnight, becoming the fifth victim of the storm. Late on Thursday, Fire and Emergency NZ (FENZ) confirmed the death of a volunteer firefighter who was critically injured when a house collapsed earlier in the week.

Australian bureaucrats revealed New Zealand formally requested aid on Thursday morning.

The deputy head of the foreign affairs department’s Pacific office said emergency management teams from both nations had been working hand in glove over the past few days to scope possible support.

“We set up yesterday a national management co-ordination function to be able to respond very quickly when the request came through and we will certainly do that,” Elizabeth Peak told senators on Thursday.

Mr Hipkins said Australia was open to giving further assistance and New Zealand wouldn’t be shy to ask.

“We’ll continue to talk to them and if we need more, I’m sure that they will send more,” he said.

By Ben McKay and Dominic Giannini in Canberra