Tonga has so far not responded to Solomons' requests to waive immunity for the soldiers although Fonokalafi and Tongan solicitor general 'Aminiasi Kefu flew to Honiara last week to meet with Solomon's attorney general Gabriel Suri.Mr Suri said Solomon Islands wants the right to charge the soldiers if necessary.
The Solomon Islands Attorney General told local reporters that there were two requests - the first was to grant a waiver on the immunity of RAMSI officers and personnel to allow his office to proceed with any possible case or charges where evidence suggests a need to lay charges.
The second request was for Tonga to give Solomon Islands the jurisdiction over the Tongan soldiers.
Tonga's Solicitor General Fonokalafi would not comment directly on the incident, although he confirmed Tonga would conduct its own investigation into the shooting.
Tonga's next deployment to the Solomons is expected to take place in December.
Meanwhile Tongan soldiers deployed with the regional peacekeeping force in the Solomon Islands have returned home, but officials said it was a scheduled move and not connected to the killing of a civilian.
AFP reports Deputy commander Toni Fonokalafi confirmed the 32 soldiers, including two alleged to have been involved in the shooting death of a civilian, left Friday at the end of their four-month tour of duty with the Regional Assistance Mission to Solomon Islands force.
The man was killed on August 12 when RAMSI troops were called to break up a rock-throwing incident in a village on the outskirts of capital Honiara.
It was the second civilian death linked to the Australian-led RAMSI force since its arrival in 2003 to end years of ethnic conflict in the Solomons.