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Heavy rain last week from a tropical depression caused severe flooding in Honiara after the Mataniko River burst its banks, washing away homes and bridges.
The Government has confirmed 21 deaths, but the toll is expected to rise; about 30 people are still missing.
An estimated 10,000 are sheltering in evacuation centres.
Honiara and other areas of Guadalcanal Province have been declared a disaster zone.
The UN Office for the Co-ordination of Humanitarian Affairs is beginning deployments to Honiara.
Pacific region chief Sune Gudnitz said the situation required urgent funding and support.
"Our immediate priority is to address the humanitarian needs of the thousands of people in emergency shelters," he said.
"Funds are needed to assist the affected population, who are from some of the poorest urban and remote communities of the country."
Honiara International Airport reopened to commercial flights yesterday, enabling the movement of aid workers and supplies.
Staff from the Save The Children charity have started to distribute items such as soap, towels and buckets to help prevent the spread of disease in the region.
Sewage systems in the capital have been wiped out. A Save The Children spokesman, Graham Kenna, said there was a high risk of disease and workers were rushing to help where they could.
"This is a huge problem for the city, but especially for the 10,000 people who are crammed into evacuation centres, having lost their homes."
Mr Kenna said the charity was very concerned for children affected by the flooding.
"Not only have many lost their family homes ... but they've suffered terribly emotionally."
At a post-Cabinet press conference in Wellington, Prime Minister John Key said assessments indicated damage to housing, power lines, roads and bridges.
New Zealand had responded swiftly with $300,000 worth of aid, which had been used by World Vision and Oxfam, which were distributing essential supplies, he said.
An RNZAF C-130 Hercules flew to the Solomons yesterday carrying relief supplies and emergency response staff from state agencies and NGOs.
"Assessment teams on the ground will report back to help shape our next steps, including consideration of what additional assistance might be required," Mr Key said.
He said the usual process was to allocate a small amount of monetary aid in the first instance until an assessment team could update the Government on what was required.
A New Zealand Police contingent on deployment to Honiara as part of the Regional Assistance Mission to the Solomon Islands had been working with the Royal Solomon Islands Police Force to assist with its response.
- Brendan Manning and Vaimoana Tapaleao