Abbas said the Palestinian government was "absolved, as of today, of all the agreements and understandings with the American and Israeli governments and of all the obligations based on these understandings and agreements, including the security ones".
Speaking after a meeting of the Palestinian leadership in Ramallah, the 85-year-old leader said Israeli annexation of any parts of the occupied West Bank would ruin chances for a two-state solution.
Abbas has made multiple previous threats to end security cooperation with Israel without ultimately following through.
He did not give any details about what his latest declaration would mean in practice.
Analysts say coordination between Israeli and Palestinian security forces in the occupied West Bank is crucial to Israel as it seeks to prevent Hamas gaining a foothold in the West Bank but also benefits the Palestinian government, which is dominated by Abbas's Fatah party - a longtime rival of Hamas.
Israeli Prime Minister Benjamin Netanyahu on Sunday swore in a new unity government with former rival Benny Gantz.
Under the coalition agreement from July the government can discuss annexing parts of the West Bank.
Right-winger Netanyahu campaigned in a March election on annexing both the Jordan Valley, a key strategic area in the West Bank, as well as settlements dotted throughout the territory.
Abbas last week said any annexation would lead them to rip up all agreements.
Follow us on Facebook, Twitter and Instagram to stay connected