The documents have been presented to UN Special Coordinator for the Middle East Peace Process Robert Serry.
"Once we receive the letters at Headquarters, we will be reviewing them to consider the appropriate next steps," UN spokesperson Farhan Haq said.
Palestinian Authority Ambassador to the UN Riyad Mansour said at the request of his government, he had delivered copies of the 15 letters to the Secretary-General's Chef de Cabinet, Susana Malcorra.
"Palestine is exercising its legal right as a State to join those instruments and live up to its international responsibility," said Mansour, recalling the November 2012 General Assembly vote according Palestine the status of non-member observer State at the UN.
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"We are proud of this and consider it a step by our President to consolidate and strengthen the pillars of the State of Palestine in the international system," he added, referring to the applications.
He, however, said the Palestinian side will continue to participate in the political process towards ending the occupations and realizing the aims of the two-state solution.
Mansour said the Palestinian leadership had been ready and willing to keep this (latest) exercise of seeking accession to the UN treaties on hold as long as Israel had lived up to its pledge to release the next group of prisoners.
"But Israel did not honour its part of the agreement and when that happened, we were free to do whatever we feel we need to do. In any case, it was our right after the adoption of the (General) Assembly resolution," he declared.