Israeli occupation forces attacked protesters using rubber bullets and teargas to suppress demonstrations in the occupied West Bank city of Bethlehem.
The Israel Prisons Service spokesman Assaf Librati said Barghouti had been transferred from Hadarim Prison to the Kishon Prison, near Haifa.
Israeli Public Security Minister Gilad Erdan vowed that authorities would not negotiate with the prisoners and said Barghouti had been placed in solitary confinement in another prison.
Hunger strikes by Palestinian prisoners occur regularly, but rarely on such a large scale.
Ramallah, Tel Aviv - On the second day of hunger strikes in Israeli prisons, officials attacked strike leader Marwan Barghouti, saying that Israel should have executed the head of the central Fatah committee a long time ago.
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He is popular among Palestinians, with polls suggesting he could win the Palestinian presidency. Their plight raised tensions between the Palestinian public and Israeli authorities.
More than 1000 Palestinians held in Israeli jails have begun a mass hunger strike against detention conditions.
Opponents of that law, including the Israel Medical Association (IMA), say that force-feeding is a form of torture and have called on doctors not to agree to force-feed prisoners.
Israeli prison officials could not be reached for comment Monday night. The Prisons Service did not initially comment on his status.
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Some 6,500 Palestinians are being held in Israeli prisons, including 300 minors, according to Palestinian human rights organization Addameer.
Erdan says the prisoners receive all privileges required by global law. In 2014, dozens of detainees held without trial went on hunger strike for two months.
A spokesperson for Israel's Foreign Ministry said in a statement Monday that the prisoners were not political prisoners, but "convicted murderers and terrorists". Nowhere is there any reference to Barghouti's leadership of the Palestinian terror group Tanzim, or his multiple murder convictions.
For Palestinians, the prisons have become a stark symbol of Israel's occupation.
The strikers also want better medical treatment and that disabled inmates or those suffering chronic illness be freed, access to more television channels and more phone contact with relatives and more family visits. The Times initially only described Barghouti as a "Palestinian leader and parliamentarian".
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Earlier this week, police in Marseille arrested two men who were allegedly plotting an attack before the election, per Reuters. Far-right candidate Marine Le Pen took to Twitter to offer her sympathy for law enforcement officers "once again targeted".
Despite - or perhaps because of - his prison sentence, Barghouti's popularity has grown among Palestinians, and he is one of the few Palestinian leaders with support from both Fatah, which governs the West Bank, and Hamas, which rules Gaza.