The suspect is the son of the head of the Nakano city council, public broadcaster NHK reported.
The individuals involved were brought before the commander of Sayeret Nahal, Col. Oren Simcha, on Sunday to receive final judgment.
"This is a serious incident that is not consistent with the IDF's values," said the IDF Spokesperson's Unit.
The president renewed calls for Congress to ban assault weapons and high-capacity magazines, as well as to enact universal background checks and end immunity for gun manufacturers.
The new regulations would need to be brought before the Knesset National Security Committee for approval.
In addition to the four people whose lives were lost, 28 people were injured, some critically.
In Rahat, a 14-year-old was shot dead and a teen was injured in a conflict between two families, while in Haifa a man was killed in a suspected hit.