Jailed Fatah leader Barghouti, who was sentenced to five life sentences for five murders plus 40 years for attempted murder, is believed to be one of the hunger strike leaders.
Intelligence and Transportation Minister Yisrael Katz said Tuesday that Barghouti, is now leading the hunger strike, should have been given the death penalty instead of life imprisonment.
It added that Israel has also installed a field clinic in the Negev desert to use for placing the ailing hunger striking detainees after deciding not to move any of them to Israeli hospitals.
A statement released by Hamas warned the Prison Service against harming the hunger strikers.
Librati said that some 1,100 detainees in several prisons had announced they were going on hunger strike.
Barghouti, who has been named as a possible successor to Palestinian President, Mahmoud Abbas, called the strike "the most peaceful form of resistance available".
"On this day, we are reminded of the pain of imprisonment, the cruelty of the occupation and the injustice of the prison cells, as we are reminded of our pride in your steadfastness and sacrifice", said Rami Hamdallah, prime minister of the Palestinian Authority in a recorded video message on his Twitter page.
The strike lasted two months, the longest mass fast in Palestinian history, and ended with an agreement that the head of the Palestinian Prisoners' Club described as "not a huge victory, but a modest step forward".
While Palestinian prisoners have mounted hunger strikes before, it has rarely on such a large scale.
Responding to global interest in the hunger strike, Israel's foreign ministry insisted in a statement: "The Palestinian prisoners are not political prisoners".
"We will not surrender to it", he wrote.
Erdan said Barghouti was transferred to another prison in northern Israel and was placed in solitary confinement.
He is popular among Palestinians, with polls suggesting he could win the Palestinian presidency.
A former leader of the Tanzim brigade - the militant wing of the Fatah political party - Barghouti was convicted in 2004 of five counts of murder, including orchestrating attacks against Israelis. Prisoners are also demanding better medical care and extended visits with family.
Prisoners' relatives told the humanitarian group that they had not seen their incarcerated family members for years, as Israeli officials frequently refused visits, citing "security grounds".
According to figures from the PNA, about 6,500 Palestinians are in 22 Israeli prisons and in detention centres, including 300 minors, 12 lawmakers and 28 journalists.