Following a meeting yesterday evening with US Secretary of State John Kerry in the West Bank city of Ramallah, "President Abbas has rejected the ideas presented by the secretary of state", the source said.
Abbas also gave Kerry a letter on "Palestinian red lines", the source added, singling out "the refusal to recognise Israel as a Jewish state".
Abbas "rejected the ideas on security because there is not a third party".
The Palestinian source said that "all disputed issues must be settled".
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Israeli and Arab media reports say the plan envisaged by Washington would see Israel maintain a military presence on the border after a peace agreement with the Palestinians.
An international force would be acceptable to the Palestinians, but Israel opposes such a solution.
Abbas's comments were made public as Kerry met Israeli Prime Minister Benjamin Netanyahu in Jerusalem in his latest attempt at promoting an elusive Israeli-Palestinian peace deal.