The move comes after the deeply divided cabinet failed to approve a commission to oversee elections planned for June.
It was also unable to agree on the extension of the term of office of the internal security chief, who is otherwise obliged to retire next month.
Lebanon has been gripped by a political crisis linked to the unrest in neighbouring Syria.
'Dangerous vacuum'
Mr Mikati said he hoped his departure would be "an impetus for leaders to shoulder their responsibilities".
He also urged political parties to "come together to bring Lebanon out of the unknown".
Mr Mikati had been pushing for the extension of the mandate of the internal security chief, Ashraf Rifi, to avoid what he described as "a dangerous vacuum".
But that was opposed by the Shia Islamist movement Hezbollah and its allies - who dominate the government.
Mr Mikati warned that internal divisions among the Lebanese had created deep wounds which only a dialogue could heal.
And he revealed that he had almost quit twice before since taking office in 2011.
President Michel Suleiman has so far made no comment on whether he will accept his resignation.
Mr Mikati became prime minister after Hezbollah and its allies brought down the unity cabinet of Saad Hariri.
Lebanon's political and sectarian divides have been heightened by the conflict in Syria, with many Sunni Muslims sympathising with the rebels there, and Hezbollah supporting President Bashar a-Assad.
