Ismail Nasreldeen caused political uproar when he proposed the term extension and lifting restrictions on running for re-election, amid fears that amending the constitution would be a prelude to a dictatorship.
But on Sunday, in a partial turnaround, the MP said his proposal would begin only with the next president.
El-Sisi, 62, took office in June 2014, so his first term ends in 10 months. He has not said if he will seek re-election although he is widely expected to do so. He is barred by the constitution from serving more than two four-year terms.
Nasreldeen announced a few months ago that he had started collecting signatures to amend article 140 of the constitution to extend presidential terms, and lift restrictions on re-election, to allow a president to run for more than the two four-year terms currently permitted.
He renewed the proposal last week, and said he would submit his request when parliament reconvenes in October after the summer recess.
Nasreldeen argues that extending the presidential term from four to six years is a necessity for countries that recently experienced democratic and economic changes, as it helps the executive authority to stay in power for longer to deliver long-term plans.
He will need the support of 20 percent of MPs for the issue to be discussed in parliament. Then, any amendment to the 2014 constitution must be approved in a nationwide referendum.
Even commentators in pro-government media were dismayed by the proposal. MP Mustafa Bakry, a staunch supporter of El-Sisi, said collecting signatures was no way to amend the constitution.
Those who wished to extend presidential terms “may have a point of view, but I see the need to adhere to the provisions of the constitution, two terms of four years only to any president,” he said
“I think President El-Sisi himself has said this more than once, and I do not think he favors any amendment in the constitution, especially to this article,” he told Al-Shorouk newspaper.
Mohammad Gomma, a political analyst at Al-Ahram Center for Strategic Studies, said an amendment to extend presidential terms might be in Egypt’s favor, since it has been undergoing political and economic turmoil.
“If the proposed change is to extend a presidential term from four to six years, this could be on the table of discussions as it may be in the favor of the country, to provide an atmosphere of stability to the current authority to deliver its plans,” he said.
“But lifting restrictions on re-election increases fears that amending the constitution is a prelude to dictatorship. Such amendments will not be in Egypt’s favor, nor its people.
“We want a peaceful transition of power,” he said, and future generations would not tolerate “political stagnation.”
Last month, El-Sisi declined to say whether he would run for a second term, only urging Egyptians to come out and vote in large numbers in next year's presidential election. He has made no comment on the calls to amend the constitution.
– additional reporting by the Associated Press