However, the Palestinian Authority and the Palestinian NGO the Palestinian Prisoners' Club said 1,500 inmates were keeping up their fast in Israeli jails.
Three hundred hunger strikers have "agreed to take food without having obtained" any of their demands, Israel's internal security minister, Gilad Erdan, told army radio.
"Negotiations are out of the question," he said, adding that 920 Palestinian prisoners remained on hunger strike.
Hundreds of Palestinians in Israeli jails launch mass hunger strike
But the head of the Palestinian NGO, Qadura Fares, said the prison service is trying to negotiate with some of the prisoners and had moved a number of hunger strikers to a jail in northern Israel for that purpose.
"The Israeli prison service is trying to launch negotiations with groups of prisoners who are on hunger strike about their demands, except for [Palestinian leader] Marwan Barghouti," said Fares.
The hunger strike began on April 17, with those taking part ingesting only water and salt. They have issued demands ranging from better medical care to phone access.
Israel policeman fired for beating Palestinian driver
Barghouti, who is very popular among Palestinians, is serving five life sentences over his role in the second Palestinian uprising.
Fares said Barghouti was placed in solitary confinement, a claim confirmed by Issa Qaraqe, head of detainees' affairs for the Palestinian Authority, according to Palestinian media.
Erdan also said the prison service planned to set up 400 medical centres inside jails "to avoid as much as possible the transfer of hunger striking detainees to civilian hospitals".
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