RNZ Pacific correspondent Georgina Kekea said the government curfew ended this morning at 7am local time, and people are now milling around.
Some people are continuing to loot the shops.
Kekea said the rioters have stolen a lot of alcohol.
RNZ Pacific correspondent Elizabeth Osifelo said the destruction is 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.