“I will announce the formation of the cabinet in its final form next Thursday,” Prime Minister Hisham Kandil said in statements carried by state news agency MENA and state TV.
He said he had briefed Mursi on his meetings with possible candidates.
The former Irrigation and Water Resources Minister was designated premier last week, despite concerns the little-known technocrat may not have the political or economic experience needed for the job.
The time it took Mursi to name his prime minister underlined how Egypt is struggling to turn new political freedoms into an effective government following the overthrow of Hosni Mubarak in a popular uprising a year and half ago.
A Muslim Brotherhood politician and Egypt’s first freely elected civilian president, Mursi is seeking to stamp his authority on a state where the military that assumed power from Mubarak still wields enormous influence.
Kandil said Mursi was in contact with the army generals on the choice of a new defense minister, a post currently occupied by Field Marshal Hussein Tantawi, who held the post for 20 years under Mubarak.