Palestinian groups and Israeli politicians have warned of clashes between security forces and protesters if one of the prisoners currently on hunger strike dies.
Some 1,600 prisoners currently on administrative detention in Israel, some for crimes against civilians, are on hunger strike to protest alleged solitary confinement, poor prison conditions and detention without trial.
Six Palestinian prisoners were said to be "at imminent risk of dying" after starving for 50 days, said the International Committee of the Red Cross.
One of the men, Thaer Halahleh, is accused of being a member of the Islamic Jihad terrorist group and has refused food or drink for almost 75 days.
"I do this for the sake of God and my homeland, my wife and daughter," Halahleh said in a letter to his family.
The Palestinian President, Mahmoud Abbas, said: "If anyone dies it would be a disaster and no one could control the situation."
Mark Regev, Benjamin Netanyahul's spokesman, raised the government's concern with prisoners using "suicide in order to instigate violence".
"From Israel's point of view, if every time someone goes on hunger strike they get a get out of jail free card, obviously that would not be sustainable," said Mr Regev.
Israel's Ha'aretz newspaper hinted on Friday at an agreement between officials and prison groups, suggesting that the hunger strike could end "in a week to 10 days".
The agreement was said to involve releasing certain prisoners from solitary confinement and allowing them to take educational courses.