Mikati's decision came after Hezbollah members of the Cabinet balked at creating a body to supervise the June parliamentary elections, The (Beirut) Daily Star reported.
The Hezbollah group also rejected Mikati's proposal to extend the term of the internal security chief.
The prime minister said he did not consult anyone before deciding to step down, saying his decision "was a personal one."
At a news conference after meeting with Sleiman, Mikati said he hoped his resignation would "be an impetus for leaders to shoulder their responsibilities," the BBC reported.
He urged political parties to unite to "bring Lebanon out of the unknown."
Mikati formed the 30-member Cabinet in June 2011, after Hezbollah and its allies brought down the unity Cabinet of Saad Hariri.