The hunger strike was called for in connection with Palestinian Prisoners Day, observed annually, but also ahead of commemorations this summer marking 50 years since the 1967 Six Day War and the start of Israel's occupation.
Hunger strikes by Palestinian prisoners occur regularly, but rarely on such a large scale. A series of protests were also being held in Palestinian cities in connection with prisoners day.
He is a popular figure among Palestinians, with polls suggesting he could win the Palestinian presidency. Graffiti showing the iconic image of his cuffed hands raised above his head flashing a peace sign while being led away by Israeli authorities can be seen in the West Bank.
"Decades of experience have proved that Israel's inhumane system of colonial and military occupation aims to break the spirit of prisoners and the nation to which they belong, by inflicting suffering on their bodies, separating them from their families and communities, using humiliating measures to compel subjugation," Barghouti wrote in a New York Times op- ed.
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Issa Qaraqe, head of prisoners affairs for the Palestinian Authority, said that "around 1,300 Palestinian prisoners" were participating in the hunger strike and the number could rise.
The Palestinian Prisoners Club NGO put the number at 1,500.
Israeli prison service spokesman Assaf Librati said that some 1,100 detainees had announced their intention to begin a hunger strike across at several prisons.
"The prisons service has started taking disciplinary measures against the strikers and in addition a number of prisoners have been transferred to separate wings," he said.
"It is to be emphasised that the (prison service) does not negotiate with prisoners."
Palestinian president Mahmud Abbas's office called on Israel to respond to the prisoners' demands for "freedom and dignity."
Barghouti's wife Fadwa told AFP at a demonstration in Ramallah that the demands were in line with "international law and recognised as part of human rights."
The last large-scale hunger strike was in February 2013, when 3,000 Palestinians refused to eat for one day to protest against the death of a fellow detainee.
Israel says it must be vigilant to prevent fresh eruptions of violence, particularly following a wave of knife, gun and car-ramming attacks that erupted in October 2015.
While many Palestinians view Barghouti as a hero, Israelis point to the bloody suicide attacks of the second intifada and his role in the uprising.