Nine ministers, including Deputy Prime Minister Manasseh Maelanga, have defected, and several backbenchers also announced they were leaving.
They claim the ruling Democratic Coalition for Change has lost faith in Sogavare's leadership.
Communications Minister Peter Shanel, a Sogavare supporter, confirmed the resignations had put the Pacific nation's government in a minority but he was confident of regaining a majority before the no-confidence vote next week.
The no-confidence motion was filed by Derek Sikua, who heads a group of independent MPs in the 50-seat parliament.
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"Governor General Sir Frank Kabui has seen the (resignation) letters and has accepted them," Ziza said.
The prime minister linked the resignations to an anti- corruption bill about to go before parliament with some MPs fearing it could lead to them being jailed.
"The move by some of the nine ministers was orchestrated in an attempt to derail the Anti-Corruption Bill (ACB)," Sogavare's office said in a statement.
"Some of these resignations come as no surprise based on the fact that some of these same ministers were responsible for undermining the progress of the ACB."
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