The Solomon Star reported 16 of the 20 former positive cases, who had been in isolation, had completed their follow-ups and been released.
Mr Sogavare told the paper the four others remained in isolation pending their follow-up tests and said all cases would be tested again 90 days after their first release into the community.
Sogavare also said the crew member diagnosed with Covid-19 on a gas supply vessel remains isolated on the ship and is not recorded in the Solomons' figures.
