Flash floods have killed at least 16 people and left some 10,000 homeless in the Solomon Islands' capital, Honiara
Save the Children says 40 people are unaccounted for and staff have witnessed a child being swept away.
Days of rain caused rivers to burst their banks late on Thursday, washing away homes and bridges and submerging large areas of Honiara.
Forecasters warn that the storm battering the South Pacific islands could develop into a tropical cyclone.
Save the Children's Graham Kenna in Honiara said: "The scale of the damage is still unclear outside Honiara as both bridges out of the city are cut off. However, in the city thousands of homes have been completely washed away, with people fleeing for their lives."
He added: "We are extremely concerned about the welfare of children across the Solomon Islands as they are particularly vulnerable during emergencies. My staff have witnessed a child being swept away by the floodwaters. They are devastated by what they have witnessed."
The agency says more than 10,000 people are sheltering in schools across Honiara with hundreds more camped out at the international terminal of the airport.
Pictures showed debris thrown on to the shore and houses washed into the swollen Matanikau and Lungga rivers.
Disaster officials said several evacuation centres had been set up.
The director of the National Disaster Management Office (NDMO), Loti Yates, told the BBC that people had lost their lives because they had failed to heed earlier government warnings to move away from river banks.
Some roads leading into the city, located on the main island of Guadalcanal, were reportedly closed.
The UN Office for the Co-ordination of Humanitarian Affairs said the floods had followed days of heavy rain, which was still falling.
"The depression is threatening to turn into a category one cyclone in the coming hours and days," regional director Sune Gudnitz told the AFP news agency.
"The water has not subsided and flood waters are continuing to build."
Solomons Prime Minister Gordon Darcy Lilo said the government would declare a state of emergency, local media report.
Loti Yates told the Solomon Islands Broadcasting Corporation that the flash floods were the worst he had seen.
"There is so much heavy rain around the area that creates massive flash foods," Mr Yates said, adding that malfunctioning drainage systems were contributing to the floods.
The NDMO has warned residents to go to higher ground or stay indoors, the Solomon Times reports.
Australia has pledged at least A$50,000 (£27,900; $46,200) in funds to support flood relief efforts.
New Zealand has given an initial contribution of NZ$300,000 (£154,500; $256,200).
New Zealand Foreign Minister Murray McCully told the New Zealand Herald that infrastructure and homes had been damaged.