Two people were killed when two simultaneous quakes hit near Christchurch on Monday morning, followed by thousands of aftershocks.
Thousands were cut off in Kaikoura after roads and infrastructure were badly damaged.
Many were tourists visiting the popular whale-watching destination.
The country has been hit by at least 1,823 earthquakes since the magnitude 7.5 earthquake on Monday, according to GeoNet, New Zealand's government-funded earthquake monitoring service.
Tonkin and Taylor, an earthquake engineering consulting firm which was employed by the New Zealand government to assess damage to Kaikoura, told the BBC that the damage in the area was "catastrophic".
"There have been 100,000 landslides, over 50 covering State Highway 1," the main road which runs the length of the country, it said.
But the company said damage to residential housing was "not too bad".
Helicopters began airlifting people from Kaikoura on Tuesday, after landslides cut off road and rail links. Power and water supplies have also been disrupted.
More than 400 people have already been evacuated by air or sea, and the defence force aims to get all people who want to leave out by the end of Wednesday, the New Zealand Herald reported.
The HMNZS Canterbury in already in the area, while HMNZS Wellington has begun surveying the seabed. The ships will be joined later on Wednesday by Canada's HMC Vancouver, Australia's HMAS Darwin and the US destroyer USS Sampson.
The USS Sampson is the first US warship to visit New Zealand in 30 years.
The foreign warships had been destined for Auckland to take part in 75th anniversary celebrations for the New Zealand navy but diverted to help with the recovery effort.
New Zealand Defence Minister Gerry Brownlee said the offer of assistance was "heartening", and that Japan and Singapore had also offered help.
Meanwhile, the cleanup is continuing in Christchurch and the capital, Wellington. Some streets remain cordoned off while safety checks are carried out.
Some buildings have been evacuated because of "structural concerns", TVNZ reported.
Fire Service regional commander Brendan Nally told commercial radio that one eight-storey office building in central Wellington would likely be demolished soon.
"The building is at significant risk of collapse so currently police and fire are conducting operation to seal off the area," he said.
Wellington Mayor Justin Lester said the full extent of damage would become clear later, but that the city had "resilience to cope" and the focus should be on "the worst affected areas".
Geonet said Monday's quake - actually two at the same time - had a magnitude of 7.5, making it the largest in the quake-prone country since 2009.
The US Geological Survey (USGS) placed it at 7.8.
New Zealand lies on the Ring of Fire, the fault line that circles virtually the entire Pacific Rim bringing frequent quakes and volcanic eruptions.
Christchurch is still recovering from a 2011 earthquake that killed 185 people and destroyed the city centre.