RNZ Pacific correspondent Elizabeth Osifelo said the destruction was focused on the city's east.
"Chinatown has now been badly affected and also the industrial area in Honiara, that has also been affected. A lot of local businesses have also gone up in flames," she said.
In a public address last night through the Solomon Islands Broadcasting Corporation, Prime Minister Manasseh Sogavare said he had been asked to step down, but this was something he would not do.
"If I have to step down, what message would that send to our people, children and generations to come?
"Some of us are of the opinion that if I step down, the protests and riots will stop, this is the easiest decision to make. However, the effect of this decision is what weighs heavy in my heart," he said.
Solomon Islands Prime Minister Manasseh Sogavare. Photo / SIG news service, RNZ
Dozens of Australian police and defence force (AFP) personnel have begun arriving in the Solomon Islands capital amid major unrest.
Australian Prime Minister Scott Morrison said the deployment was in response to a request from Sogavare as part of a security treaty signed with Australia in 2017.
He said the 23 AFP personnel would help with riot control, and up to another 50 would be deployed to support security at critical infrastructure.
Morrison said he had spoken to the leaders of New Zealand, Fiji and Papua New Guinea to discuss how peace and stability can be restored.
Australia's Prime Minister Scott Morrison. Photo / screenshot, SBS TV, RNZ
"That our purpose here is to provide stability and security to enable the normal constitution processes within the Solomon Islands to be able deal with the various issues that have arisen, and that it be done in a climate of peace and security," he said.
Morrison said Australia's assistance would not result in it interfering in the internal affairs of Solomon Islands.
