Solomon Islands acting Commissioner of Police, John Homelo, says officers are investigating the shooting incident at the residence of the Prime Minister in Honiara late last week.
A group of special constables, who are demanding outstanding payments from the government, fired several shots at the Prime Minister's residence at Vavaya Ridge.
The Prime Minister, Sir Allan Kemakeza, was in the building at the time, but he was not injured.
Mr Homelo told the Solomon Islands Broadcasting Corporation that one of the special constables has been arrested and the Criminal Investigation Department is now dealing with the case.
He says he held a meeting with some of the special constables over the weekend and asked them to be patient while the Government tries to address some of their demands.
