Health authorities confirmed the country's first two deaths on Tuesday.
During a media conference on Thursday night, Health Minister Dr Culwick Togamana, said they are expecting more cases in the coming days.
He said community transmission was now widespread in the capital Honiara and some provincial areas.
"For the Western Province, a surge in flu-like illness was noted in Rukutu Village where we suspect a recent gathering involving those who travelled from Honiara and may have transmitted Covid-19.
