Abbas was in Cairo to address the Arab League, which backed the Palestinians in their opposition to Trump's plan.
The blueprint, endorsed by Israeli Prime Minister Benjamin Netanyahu, calls for the creation of a demilitarised Palestinian state that excludes Jewish settlements built in occupied territory and is under near-total Israeli security control.
“We've informed the Israeli side ... that there will be no relations at all with them and the United States including security ties,” Abbas told the one-day emergency meeting, called to discuss Trump's plan. Israeli officials had no immediate comment on his remarks.
Israel and the Palestinian Authority's security forces have long cooperated in policing areas of the occupied West Bank that are under Palestinian control. The PA also has intelligence cooperation agreements with the CIA, which continued even after the Palestinians began boycotting the Trump administration's peace efforts in 2017.
Abbas also said he had refused to discuss the plan with Trump by phone, or to receive even a copy of it to study it: “Trump asked that I speak to him by phone but I said 'no', and that he wants to send me a letter ... but I refused it.”
Abbas said he did not want Trump to be able to say that he, Abbas, had been consulted. He reiterated his “complete” rejection of the Trump plan, presented on Tuesday.
The blueprint also proposes US recognition of Israeli settlements on occupied West Bank land and of Jerusalem as Israel's indivisible capital.
The Arab League foreign ministers meeting in Cairo said the plan would not lead to a comprehensive and just peace, and that the League would not cooperate with the US in implementing it.
The ministers affirmed Palestinian rights to create a future state based on the land captured and occupied by Israel in the 1967 Middle East war, with East Jerusalem as capital, the final communique said.
Foreign ministers from Egypt, Saudi Arabia, Jordan, Iraq, Lebanon, among others, said there could be no peace without recognising Palestinian rights and a comprehensive solution.
After Trump unveiled his plan, some Arab powers had appeared, despite historic support for the Palestinians, to prioritise close ties with the US and a shared hostility towards Iran over traditional Arab alliances.
Three Gulf Arab states — Oman, Bahrain and the United Arab Emirates — attended the White House gathering where Trump announced his plan alongside Netanyahu.
On Tuesday, Netanyahu said he would ask his cabinet this week to approve the application of Israeli law to Jewish settlements in the West Bank.
Such a move could be a first step towards formal annexation of the settlements and the Jordan Valley — territory Israel has kept under military occupation since its capture in 1967.
Most countries consider Israeli settlements on land captured in war to be a violation of international law. Trump has changed US policy to withdraw such objections.
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