Prime minister Manasseh Sogavare said those behind yesterday's scenes of destruction in Honiara would be held accountable.
He gave a national address following the protests, which led to crowds breaching parliament's precinct and burnt a building next to the main chamber.
It was followed by looting and burning of properties in town, including a school and a police station.
Sogavare announced a full lockdown until Friday, and assured the public of their safety.
"I assure you all that the people responsible for today's events which lead to the destruction of properties will be taken to justice and they will face the full brunt of the law.
"No one is above the law."
The protest was led by citizens from Malaita Island, who voiced frustrations with the national government and called for Sogavare to step down.
Guadalcanal province premier Francis Sade called for an end to the unrest, and said there were peaceful ways to properly address differences through democratic means.
Political violence was not a solution for diverse and close-knit communities like Honiara and Henderson, he said.
And he asked all provincial and national leaders in the Solomons to make the same calls to quell the ongoing tensions.