Analysts were quick to question whether Abbas seriously intended to deliver on the threat which has been made several times in the past.
But the Palestinian leader had not previously spoken so clearly and definitively of a break in cooperation.
What are the agreements with Israel and will Abbas's comments change anything?
What did Abbas say?
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President Abbas spoke Thursday night after a week in which Israel destroyed 12 Palestinian residential buildings in Sur Baher, a neighbourhood that straddles annexed east Jerusalem and the occupied West Bank.
Israel said the buildings, many of which were still under construction, built too close to the separation fence that cuts off the West Bank, but Abbas on Thursday labelled them an act of "ethnic cleansing."
Some of the buildings are in an area meant to be fully under the control of Abbas's government, and he said it was further evidence Israel was not respecting agreements between them.
In response, the 84-year-old said, "we announce the leadership's decision to stop implementing the agreements signed with the Israeli side."
He said a committee would be formed immediately to implement the decision.
What are the agreements?
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In the early 1990s Israel and the Palestine Liberation Organization, then headed by Yasser Arafat, signed a number of peace agreements under US sponsorship.
Abbas was a key figure in negotiating the so-called Oslo Accords.
They led to the creation of the Palestinian Authority (PA) and cover a range of issues including water usage, electricity, security coordination and economic relations between the two sides.
The agreements were supposed to be for a transitional five-year period but a longer-term deal proved elusive and a second bloody Palestinian intifada, or uprising, broke out in 2000.
Abbas took power after Arafat's death in 2004 and pledged to pursue peaceful measures only, with the agreements once again becoming the de facto basis of the relationship between the PA and Israel.
Abbas has since pursued a policy of diplomatic recognition, earning Palestine observer status at the United Nations in 2012.
Ripping up the agreements could seriously impact security in the occupied West Bank, where more than 400,000 Israelis live in settlements alongside some 2.6 million Palestinians.
Why now?
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Relations between Abbas's government, based in the West Bank, and its Israeli counterpart have worsened in recent months.
In addition to the house demolitions Israel has also started deducting around $10 million a month from tax revenues it collects on behalf of the Palestinians.
That corresponds to the amount it says the PA pays to families of prisoners or directly to inmates in Israeli jails.
Israel sees such payments as encouraging attacks while Palestinians see them as support for families who have often lost their main breadwinner.
The Palestinians have in response refused to take any of the roughly $180 million in monthly tax revenues until the full amount is transferred, leaving Abbas's PA in financial crisis.
Will they follow through?
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Palestinian officials have previously made a number of threats to cut relations with Israel.
In January last year, the Palestinian Central Council voted to suspend recognition of Israel, but the decision has yet to be implemented.
Thursday's comments were the most direct by Abbas himself regarding the agreements but there is scepticism that he will follow through.
Ending the agreements could lead to the demise of the Palestinian Authority of which he is president.
"It is useless to talk about halting agreements with Israel without talking about the fate of the Palestinian Authority and changing its shape and functions," said analyst Hani al-Masri.
"The resolution is a repetition of previous resolutions."