The motion was triggered by a series of defections from Mr Sogavare's coalition government late last month.
Beginning the debate, opposition MP Derek Sikua outlined to parliament his reasons for tabling the motion.
Dr Sikua said MPs had lost confidence in the prime minister because he wasn't listening to them any more.
He said Mr Sogavare has become suspicious of anyone who differs from his point of view.
"Once he is fixated on a conspiracy his judgement, Mr Speaker, inevitably becomes subjective to it. My greatest sadness is that all too often, the prime minister sees it fit to lower himself to submit to advice from individuals with dubious character."
After four hours of debate, a vote is expected soon.