Mr Hamdok called for a dialogue to agree on a "national charter" and to "draw a road map” to complete the transition.
The October coup upended Sudan's plans to move to democracy after a popular uprising forced the military's overthrow of long-time autocrat Omar al-Bashir and his Islamist government in April 2019.
On Sunday, prior to his resignation, Sudanese security forces violently dispersed pro-democracy protesters, in the latest demonstrations to denounce the takeover and a subsequent deal that reinstated the prime minister but sidelined the pro-democracy movement.
A medical group said at least two people were killed.
The Sudan Doctors Committee, which is part of the pro-democracy movement, said one of the dead was hit "violently" in the head while taking part in a protest march in Khartoum.
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