The amendments would extend al-Sissi’s current term from four to six years, to end in 2024.
A provisional article allows him to run for a third term, potentially staying in power until 2030.
The changes allow the president to appoint senior judicial positions and also envisage a bigger role for the army.
The changes must be approved by at least two-thirds of the 596-strong House of Representatives before they are put to a public referendum.
The legislature is dominated by al-Sissi loyalists.
Proponents say the changes are necessary for long-lasting stability in Egypt.
But opponents say the amendments are aimed at tightening al-Sissi’s hold on power and breach the judiciary’s independence.
Al-Sissi took office in 2014, a year after he led the army’s ouster of former President Mohammed Morsi following mass protests against his rule.