The cyclone hit the North Island's uppermost region on Feb. 12 and tracked down the east coast, inflicting widespread devastation. Prime Minister Chris Hipkins has called Gabrielle New Zealand's biggest natural disaster this century.
On Sunday, police said two more people had died in the hard-hit Hawke's Bay area in circumstances related to the cyclone, raising the death toll to 11.
Some 5,608 people remained uncontactable across the country, while 1,196 had registered they were safe, police said.
Authorities have previously said they have grave fears for a small number, around 10, of those still missing.
Recovery efforts continued, with teams from Auckland Council carrying out rapid building assessments on damaged homes in the coastal areas of Muriwai and Piha, about 60 km (40 miles) west of the nation's largest city Auckland.
Emergency authorities and military on Saturday dropped critical supplies via helicopter to communities stranded since the cyclone, which washed away farms, bridges and livestock and inundated homes.
Around 62,000 households were without power nationwide on Saturday. Of those, almost 40,000 were in Hawke's Bay, out of a population of about 170,000.
Prime Minister Hipkins has said the crisis response is "still underway" and that people across the North Island are "working around the clock."
Police have sent an extra 100 officers to Hawke's Bay and nearby Tairawhiti, including to isolated areas, and the New Zealand Herald reported roadblocks around a rural Hawke’s Bay village to deter looters.
"Targeting people in a crisis is abhorrent and we’re not tolerating it," police Superintendent Jeanette Park said.