He has asked the premier to stay on as a caretaker until a new government can be formed.
Lebanon's president on Saturday asked the outgoing prime minister to stay on in a caretaking role, opening the way for what is expected to be prolonged political jockeying as parliamentary blocs try to build a majority coalition to form a new government.
Prime Minister Najib Mikati's abrupt departure has plunged the nation into uncertainty amid heightened sectarian tensions and clashes related to the civil war next door in Syria.
Sporadic clashes continued in the northern city of Tripoli between supporters and opponents of Syrian President Bashar Assad. At least one person was wounded Saturday, according to the state-run National News Agency.
Mikati stepped down on Friday amid a political deadlock between Lebanon's two main political camps and infighting within his own government.
"I hope that this resignation will provide an opening in the existing deadlock and pave the way for a (political) solution," Mikati said, following a meeting with Michel Suleiman.
Mikati has been prime minister since June 2011, heading a government dominated by the Shiite militant group Hezbollah and its allies, many of whom have a close relationship with Syria.
Their main rivals are a Western-backed coalition headed by former Prime Minister Saad al-Hariri, son of Rafik Hariri, who was also prime minister and was killed in a truck bombing in 2005.
A Harvard-educated billionaire, Mikati was chosen to lead the government after Hezbollah forced the collapse of Lebanon's previous, pro-Western government over fears that a U.N.-backed tribunal investigating the killing of the elder Hariri would indict Hezbollah members.