Much of the capital Honiara was inundated as thousands of people took refuge in emergency shelters.
A state of emergency has been declared amid concerns over food and water supplies and damaged infrastructure.
Solomons Red Cross Secretary General Joanne Zoleveke described the floods as “a tragedy none of us saw coming”.
Honiara’s main river, the Matanikau, burst its banks in the storm, sweeping away houses and bridges and flooding the downtown area.
Eleven evacuation centers have been set up at schools and at Honiara’s international airport, the World Vision aid agency says.
It says that the domestic airport terminal is under water and there are fears about the spread of disease once the water subsides.
Other parts of Guadalcanal province – where the capital is located – have also been declared disaster zones, officials say.
“Clean water sources have been contaminated, sanitation facilities destroyed and there is a lack of medicines to treat people who get sick,” said Lawrence Hillary, World Vision’s emergency response manager in the islands.
While water levels were reported to be subsiding on Saturday, aid agencies have warned that police still face the unpleasant task of finding more bodies in seaside and river debris.
The official number of deaths was, however, lowered on Saturday to 12 from the previous day’s toll of 16.
The impact of the flood was made worse because it struck so fast, giving people little time to escape from their homes.
Save the Children said on Friday that the scale of the damage was still unclear outside Honiara as both bridges out of the city had been cut off. However, it says that in the city itself thousands of homes have been completely washed away.
Australia has pledged at least A$50,000 ($46,200) in funds to support flood relief efforts.
New Zealand has given an initial contribution of NZ$300,000 ($256,200).
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