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. Many are held under the Administrative Detention provision, which allows suspects to be held without charge for six months, BBC reported.
Israel says it must be vigilant to prevent fresh violence, particularly following a wave of knife, gun and car-ramming attacks that erupted in October 2015.
The Israel Prison Service said that it does not negotiate with prisoners.
A Palestinian Authority official said that the "strike was called for by Fatah leader and prominent prisoner Marwan Barghouti".
It was unclear whether the strike could be sustained to the point of forcing concessions from the Israeli authorities, but experts said it nonetheless had the potential to stir passions among Palestinians.
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On Monday, the Israeli Foreign Ministry complained that jailed Palestinians should not be described as "political prisoners".
Demonstrators gather during a rally in support of Palestinian prisoners on hunger strike in Israeli jails, in the West Bank city of Ramallah April 17, 2017.
On Saturday, Amnesty International that "Israel's decades-long policy of detaining Palestinians from the occupied West Bank and Gaza in prisons inside Israel and depriving them of regular family visits is not only cruel but also a blatant violation of international law". "In spite of such treatment, we will not surrender to it".
More hardline still was the reaction by Israel's intelligence and transportation minister, who tweeted that Barghouti should have been executed after his conviction for murder in 2004 in an Israeli court.
Furthermore, Israeli has moved at least 35 detainees from Section 11 to Section 13, in Nafha Israeli prison, in addition to transferring what it regards as "strike leaders" to various other prisons, and forced many of them into solitary confinement.
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The hunger-striking prisoners were calling for better conditions including access to phones, better medical services and extended visiting rights for their families.
This includes 300 minors and more than 500 administrative detainees.
Opinion polls suggest Barghouti is the top contender to succeed Mr Abbas as president.
Israeli Prime Minister Benjamin Netanyahu criticized the New York Times after the newspaper published an op-ed written by Palestinian terrorist Marwan Barghouti.
"This massive strike sends a strong message to the Israelis, after 50 years of occupation, suppression and oppression, that the prisoners. will lead their people from behind bars", she said.
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