"The Israelis want chaos and we know it but we won't let them," Abbas said in comments at his West Bank headquarters, seemingly in response to an Israeli demand on Sunday that he calm a wave of protest in the territory.
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"We want peace and freedom for our prisoners and no matter how hard they try to drag us into their schemes, we will not be dragged," he said.
Protests in support of Palestinian prisoners on hunger strike in Israeli prisons have been building and gained new momentum with the sudden death of Arafat Jaradat, a former militant of Abbas's Fatah movement, in his cell on Saturday.
Palestinian officials accuse Israel of torturing him to death.
"We lost Arafat Jaradat who was arrested and came back in a coffin and this cannot pass lightly," Abbas said.
On Sunday, Prime Minister Benjamin Netanyahu's office relayed Israel's demand that the Palestinian Authority take all the necessary measures to calm the situation on the ground.
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