"My guess is that the military would like to retain as much control as possible for as long as possible, still accepting the results of the revolution and the election process that's underway," Carter said in the Egyptian capital Cairo on Thursday.
The ruling Supreme Council of Armed Forces took over after the ouster of the former Egyptian dictator Hosni Mubarak in a popular revolution in February.
He added that the Muslim Brotherhood and other political parties, however, might allow the military to keep power for a limited period of time.
The Carter Center, which is a nongovernmental, non-profit organization founded in 1982 by Carter and his wife Rosalynn Carter, have deployed forty observers in Egypt since November, throughout the course of its three stage parliamentary election process.
Egypt embarked on a three stage parliamentary elections in late November 2011. The final stage ended this week.
The Freedom and Justice Party of the Muslim Brotherhood said on Saturday that it had garnered 35.2 percent of the party list vote in the final stage of the election. Another Islamic party al-Nur said it received 27 percent in the poll held on January 4.
Carter also met with the Freedom and Justice Party's chairman Mohamed Mursi and discussed power transition process.
The former US president also congratulated Mursi on the great showing in the elections.