Nano's resignation was announced after a meeting of the Socialist Party leadership in the Albanian capital.
A statement said that Pandeli Majko, the 31-year-old general-secretary of the Socialist Party, would be the party's candidate for prime minister.
The resignation came two days after former Albanian President Sali Berisha promised thousands of supporters that street protests would continue until the government steps down.
Speaking in the capital before a crowd of about 3,000 people, Berisha called Nano a "killer," and blamed him for the current political turmoil.
The unrest in Europe's poorest country erupted after a popular opposition leader was killed outside Berisha's Democratic Party headquarters on September 12. Berisha blamed his political rival Nano for the killing and demanded his resignation.
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