The government declared a state of emergency after the city's main river, the Matanikau, burst its banks late yesterday, sweeping away entire communities, bringing down bridges and inundating the downtown area.
"This is the worst disaster the nation has seen," the Solomons Star newspaper said.
Save the Children's Solomons development programme director Rudaba Khondker described the situation as "dire".
"This level of rain has never been experienced before in Guadalcanal (the island where Honiara is located)," she told AFP.
"It's a logistical challenge," she said, adding that roads had been cut and communications were patchy. "The east side (of the city) is tough to reach and in the west side we're still carrying out assessments."
She said dengue fever, already common on the Solomons, was a major concern in the evacuation camps.
The National Disaster Management Office (NDMO) put the official death toll at six late today, with another 30 listed as missing, although some reports said the number of fatalities had already reached 16.
He said the Solomons had declared a state of emergency but not yet asked for assistance from overseas, adding that such a request could be made at any time.
UN Office for the Coordination of Humanitarian Affairs' (OCHA) regional director Sune Gudnitz said the flooding followed days of heavy rain which was still falling.
"The water has not subsided and flood waters are continuing to build," he told AFP.
"The depression is threatening to turn into a category one cyclone in the coming hours and days."
Gudnitz said there was still virtually no information from areas of Guadalcanal outside Honiara, and it was likely communities elsewhere had also been severely affected.
Australia updated its travel advice for the Solomons warning the flooding had closed Honiara's Henderson International Airport and cut roads throughout the capital.
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