The composition of the new cabinet is expected to be announced this weekend.
The main opposition party, the Islamic Action Front, wants the powers of King Abdallah to be curbed and more power given to parliament.
On Tuesday Abdullah named 64-year-old Maruf Bakhit as prime minister after sacking the government of Samir Rifai.
The move followed weeks of protests to demand political and economic reforms.
The king has ordered the new prime minister to take "practical, quick and tangible steps to launch true political reforms".