"Today I went to the president and asked him to choose another candidate for the position," Grigol Mgaloblishvili said live on Georgian TV.
Mgaloblishvili, 35, who was named the head of government in November, said he had suggested the president appoint Finance Minister Nika Gilauri as the new prime minister.
The Georgian prime minister, who was ambassador to Turkey for four years, has been diagnosed with kidney disease and traveled to Germany for medical treatment in December.
Having returned to Tbilisi on January 17, Mgaloblishvili felt ill again due to high blood pressure and underwent a week of treatment in Germany.
Media reports in December said Mgaloblishvili submitted his resignation after a row with Mikheil Saakashvili during which the Georgian president hit him in the face and threw a phone at him.
The president slammed the report as "complete nonsense" and said the prime minister's illness was due to the "heavy stress" of the job.