The men were still alive when emergency crews arrived at the scene, but later died in a hospital, the outlet reported.
Atkinson, 57, from London, was a program director working to create a database of remnants of past warfare, while Lee, an Australian in his 40s, was a chemical weapons advisor for the project, reported the Telegraph.
Several unexploded bombs were found inside the apartment after the explosion.
“We are concerned that they have decided to conduct explosive ordnance disposal operations in a residential area,” Police Inspector Clifford Tunuki told The Guardian.
Norwegian People’s Aid called the incident a “tragic accident” in a statement.
“So far we know there has been an explosion with fatal consequences,” the group said. “Our main priority now is to offer assistance to parents and colleagues, and to clarify what has happened.”
The Solomon Islands was the site of a major military battlefield during the war, and its islands are dotted with unexploded bombs from the conflict, the Telegraph reported.
“There is a global problem with remnants of war, all kinds of ammunition is left behind after a conflict and it wreaks enormous havoc on societies,” said Per Nergaard, who is the group’s deputy general secretary.
“We have been doing this for 25 years. We are among the most important in the humanitarian field. “