The death toll from flash floods in the Solomon Islands climbed to 23 on Tuesday, officials said, as aid agencies scrambled to distribute supplies to thousands left homeless by the disaster.

Health kits were being handed out to 10,000 people sheltering in evacuation centres in the capital Honiara in a bid to prevent disease outbreaks, the UN Office for the Coordination of Humanitarian Affairs (OCHA) said.

As many as 40 people are still missing in the Pacific island city after the Matanikau burst its banks Thursday following days of heavy rain, creating a torrent of water that swept away entire communities.

Three military cargo planes filled with humanitarian supplies have arrived from New Zealand and Australia this week and OCHA said more aid was beginning to arrive now that Honiara's main airport had reopened.

Australian Foreign Minister Julie Bishop announced a Aus$3 million (US$2.8 million) aid package.

"The Solomon Islands government has informed us that this is the worst flood disaster they have experienced in their capital, Honiara," she said.

New Zealand Foreign Minister Murray McCully announced a further NZ$1.2 million ($1.0 million) in aid funding, bringing the country's total contribution to NZ$1.5 million.

"The additional funding will be used to provide relief supplies and help restore health, water and sanitation systems -- it is now clear that these are areas of critical need."

Save the Children has reported cases of diarrhoea and conjunctivitis in the evacuation centres while the main concern is mosquito-borne dengue fever, which was already prevalent in Honiara before the floods.