Inspector Clifford Tunuki from the Royal Solomon Islands police force said police had secured the scene and forensic investigators would determine what had caused the blast.
"Our main priority now is to offer assistance to relatives and colleagues, and to clarify what has happened", she added.
Police said they are still investigating but believe the men had several unexploded bombs at the office and may have been carrying out work to disarm them. They were rushed to Honiara's National Referral Hospital.
Both were employees of non-governmental organisation Norwegian People's Aid (NPA), whose Secretary General, Killi Westhrin, said that it was "devastated by what has happened". "RSIPF did not know these items had been moved to the NPA residence".
"On behalf of the Royal Solomon Islands police force I wish to convey my honest condolences to the family and relatives of those two foreign nationals who died in this tragic incident".
Aerial view photograph of small islands in the Solomon Islands.
NPA was working with Solomon Islands police to survey the scale of the problem and develop a nation-wide collection programme.
Following the blast, residents rushed to the scene to find the men seriously injured, the Solomons Star newspaper reported.
"The survey team goes out to confirm the location of the unexploded ordnance following reports from the communities and the information is relayed to us".
Police said they have a close working relationship with the agency.
"On behalf of the RSIPF I wish to convey my honest condolences to family and relatives of those two foreign nationals who died in this tragic incident", Tunuki said.
The Solomon islands is heavily contaminated with unexploded shells, landmines and other munitions after World War II.
"Explosive weapons are often found within city construction sites, coral reefs, farms, forests and suburban gardens where children sometimes find and play with them".