"The Palestinian leadership has unanimously approved a decision to seek membership of 15 UN agencies and international treaties, beginning with the Fourth Geneva Convention," Abbas said on television after signing the demand during a meeting at his Ramallah headquarters.
"The demands (for membership) will be sent immediately" to the relevant agencies, he said.
"This is not a move against America, or any other party -- it is our right, and we agreed to suspend it for nine months," said Abbas.
In return, Israel agreed to release 104 long-serving Palestinian prisoners.
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But Israel has refused to release the final batch of 26 prisoners, using it as a bargaining chip to try and extend talks beyond their April 29 deadline.
The Palestinians have also repeatedly threatened to resume their action through international courts and the UN over Israel's settlement expansion on occupied territory in the West Bank and in annexed Arab east Jerusalem.
Prior to Abbas' announcement, Kerry had been due back in the region for a meeting with the Palestinian president tomorrow, after a whirlwind visit yesterday and today.