The strike, which began on April 17, followed a call by Marwan Barghouti, the most high-profile Palestinian in Israeli detention, for a protest against poor conditions and an Israeli policy of detention without trial.
Earlier this week, Israel’s prison service released a video which appears to show Barghouti eating in his prison cell during the strike.
On Thursday, the Fatah Central Committee called for a further 2,500 prisoners to join the hunger strike.
The prisoners participating in the hunger strike are from various Palestinian political factions, including Fatah, the Popular Front for the Liberation of Palestine (PFLP), and some members of the Islamist terror group Hamas.
Barghouti, a leader of the Fatah movement, has seen his popularity grow among Palestinians since he was convicted of murder over the killing of Israelis during the Second Intifada and sentenced in 2004 to five life terms.
In April, around 100 prisoners belonging to the Fatah party ended their hunger strike, according to the Israel Prisons Service.
There are around 6,500 Palestinians in Israeli jails, many of whom were convicted of attacks or planning attacks against Israel.