In a speech late Tuesday, Abbas said the annexation plans showed Israel was no longer abiding by peace accords between the two.
As such, he said, the Palestinian government was "absolved, as of today, of all the agreements and understandings” with America and Israel and “of all the obligations based on these understandings and agreements, including the security ones", AFP reported.
A genuine end to security coordination could jeopardize the relative calm in the West Bank, where 2.7 million Palestinians and more than 400,000 Israeli settlers live.
Israel controls all access to the territory where Abbas's government is based.
The declaration comes as international opposition to the Israeli plans of annexations in the occupied West Bank grows.
US Democratic presidential nominee Joe Biden on Tuesday became the latest high-profile figure to oppose Prime Minister Benjamin Netanyahu's plan to apply Israeli sovereignty to settlements and the strategic Jordan Valley, which makes up around 30 percent of the West Bank.
Palestinians say any annexation would put an end to their hopes of an independent state, the so-called two-state solution.
Netanyahu has been emboldened by the staunch support of US President Donald Trump, whose controversial peace plan released in January gave Israel US approval to annex swathes of the West Bank.
But Trump's challenger in November's presidential election, Biden, on Tuesday declared his opposition to annexation, saying it would undermine hopes for peace.
Under the coalition agreement Netanyahu signed with rival-turned-partner Benny Gantz, the two can bring annexation to cabinet for discussion from July 1.
King Abdullah II of Jordan, one of only two Arab states to have signed a peace deal with Israel, warned last week annexation would put it on course for a "conflict" with his country.
Britain, Germany, and other European governments have also come out in firm opposition to the annexation plans.
Former Israeli ambassador to Jordan, Oded Eran, said Israel was wary of jeopardizing relations with the king.
Netanyahu's centrist coalition partner Gantz is far less keen on annexation than the prime minister and could also hold it back, Eran said.