On Friday, Abbas appointed three new ministers and reappointed Salam Fayyad as prime minister after he formally stepped down, aides said.
The caretaker government is set to remain in place until Fayyad forms a new administration.
Bahar has convened a special session of parliament on Sunday to challenge Abbas's decision.
"The refusal by the US, EU et al to deal with Hamas reflects their disrespect for the wishes of the Palestinian people"
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Any new government requires parliament approval under the Palestinian constitution. However, the legislature has been paralysed as a result of the power struggle between Hamas and Abbas's Fatah movement.
Hamas formally holds a majority, with 74 of 132 parliament seats.
However, in the past year, more than three dozen Hamas politicians were arrested by Israel, giving Fatah a slim majority among legislators able to attend.
Salah Bardawil, the head of Hamas's parliamentary bloc, said that the movement has obtained a written authorisation from imprisoned Hamas politicians allowing Bahar can vote on their behalf.
Abdullah Abdullah, a Fatah politician, said he and his colleagues consider Sunday's session illegal and will stay away.
Abbas and the new government only maintain effective power in the West Bank as Ismail Haniya, prime minister in the Hamas-led unity governent, has refused to accept his dismissal.
Security forces loyal to Abbas were pushed out of the Gaza Strip during violent clashes in June leaving the new government with very little authority over the territory.