"We have nine bodies and a lot of people are still missing," Dr Alex Munamua at the Solomons' National Referral Hospital said.
Local media said about 30 people remained unaccounted for following Thursday's flooding.
As about 10,000 people packed into emergency shelters, the Red Cross secretary general in the Solomons, Joanne Zoleveke, described the devastation as "a tragedy none of us saw coming".
The city's main river, the Matanikau, burst its banks in a torrential tropical storm late Thursday, sweeping away riverside communities, bringing down bridges and inundating the downtown area.
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Local resident Paul Lega told the Solomon Star newspaper the river rose too fast for some families to escape.
"I witnessed a mother and two children swept away in their home," he said as the newspaper described the devastation as "the worst disaster the nation has seen".
World Vision's Emergency Response Manager in the Solomon Islands, Lawrence Hillary, told Fairfax News the organisation was particularly concerned about the welfare of children.
"My staff has witnessed a child being swept away by the floodwaters. They are devastated by what they have witnessed."
The flooding had cut off roads throughout Honiara and of the two main bridges crossing the Matanikau, one was washed away and the other was closed after large cracks appeared in the structure.
The loss of the bridges prevented officials from getting a look at the scale of destruction in outlying areas where landslides and floods were also reported.
As Solomon Islanders battled the floodwaters they were also shaken by a strong 6.0 magnitude earthquake late on Friday, but there were no reports of any damage.