Mahlab said he was "officially tasked with forming a new government" by interim president Adly Mansour, the state-run Al-Ahram newspaper reported on its website.
He said he would immediately start consultations on the appointment of a new cabinet.
Mahlab, who resigned as housing minister yesterday, was a member of the National Democratic Party of Mubarak, whose 30-year reign came to an end with the 2011 popular uprising.
Now in his sixties, Mahlab is a civil engineer who formerly served as chairman and chief executive of the Arab Contractors Company, a large Egyptian civil engineering firm.
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Beblawi announced the decision after a cabinet meeting attended by Sisi, also the Defence Minister.
Beblawi gave no particular reason for the Cabinet's resignation, but it comes amid a series of strikes, including one by public sector workers.
Sisi is widely tipped to win the poll if he stands. He has not yet announced his candidacy but media reports said he has decided to run and will make an announcement soon.
A reshuffle to allow Sisi to step aside was on the cards but the mass resignation of the entire cabinet caught everyone by surprise including officials.