In a sharply worded attack on Hamas, Abbas on Saturday threatened to break off the unity agreement over the group's de facto control of the Gaza Strip.
But Abbas's words sparked an angry response from Hamas, with spokesman Fawzi Barhum accusing him in turn of trying "to destroy the reconciliation and play into the hands of the Americans and the Israelis."
Hamas forcibly took over the Gaza Strip in 2007, ousting forces loyal to Abbas and sparking a bitter and bloody split with his Fatah movement, which continued for years until the two sides signed a reconciliation deal in April.
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The deal led to the formation of a government of national consensus, which took office on June 2, following which Gaza's Hamas government formally stepped down.
The spat erupted just two weeks after the end of a major 50-day conflict between Israel and Hamas militants in Gaza.
Throughout the conflict, Hamas and Fatah put up a united front, working side-by-side to further indirect truce talks with Israel in Cairo, which resulted in an open-ended ceasefire that took effect on August 26.
But as the guns fell silent, their long-held divisions again came to the fore.