The pair are both part of the OUR Party, the largest party in parliament following the 2024 national election.
During government negotiations, Mr Sogavare stepped down as leader, allowing Mr Manele to become prime minister of a three-party grouping.
However, it appears that unity has been broken, with In-depth Solomons reporting Mr Sogavare is negotiating with opposition MPs.
The four other ministers to resign include Manasseh Maelanga (infrastructure), Nestor Ghiro (fisheries), Rollen Seleso (rural development) and Freda Tuki (women and youth).
Last December, Mr Manele was threatened with a no-confidence motion brought by Honiara-based MP Gordon Darcy Lilo, who withdrew it at the last minute, urging improved government performance.
The week after, Australian Prime Minister Anthony Albanese announced a $190 million investment to strengthen local policing.
Political instability is nothing new in the Solomon Islands, which has had 11 changes of prime minister this century.
Mr Sogavare has served three previous stints as prime minister.
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