Agca, 48, was freed Jan. 12 after serving nearly 25 years in jail, but a week later, a court ruled he should serve more time for killing a Turkish journalist in 1979. Agca was awaiting trial for the murder of left-wing Turkish journalist Abdi Ipekci when he escaped from prison and shot the pope in 1981.
He will remain in prison until January 2010, the BBC said.
Agca's sister, Fatma Yildirim, speaking from her home in Malatya, said 15 family members, including nine children as young as 4 had started the hunger strike to demand his release.
"Where are justice and the law? He will die in prison and we will die here," Yildirim said.