Hamdok, who had failed to name a government as protests continued against a military takeover in October, said a roundtable discussion was needed to produce a new agreement for Sudan's political transition to democracy.
"I decided to give back the responsibility and announce my resignation as prime minister, and give a chance to another man or woman of this noble country to ... help it pass through what’s left of the transitional period to a civilian democratic country," Hamdok said in a televised address.
The announcement throws Sudan's political future even deeper into uncertainty, three years after an uprising that led to the overthrow of long-time leader Omar al-Bashir.
An economist and former United Nations official, Hamdok became prime minister under a power-sharing agreement between the military and civilians following Bashir's overthrow.
Ousted and placed under house arrest by the military during a coup on Oct. 25, he was reinstated in November.