Mohammed Dahlan, once a leading figure in Abbas's Fatah party but now in exile in Dubai, took to his Facebook page to criticise the Palestinian president.
His comments came after Abbas resigned Saturday as head of the Palestine Liberation Organisation's Executive Committee in a bid to force new elections for the top body.
His resignation along with more than half of the 18-member committee will only take effect with a meeting of the Palestine National Council.
The opposition saw Abbas's move as a political manoeuvre aimed at empowering his allies and marginalising opponents ahead of the 80-year-old's eventual retirement.
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Dahlan, Fatah's former strongman in Gaza, however said the resignation of Abbas must be accepted and the future congress should "declare null and void all decisions by Abbas and his allies because they are illegal".
It should also "declare the State of Palestine and immediately call presidential and legislative elections," he said.
He fell from grace in June 2007 after the humiliating rout of his forces by Hamas in week-long street battles that saw the Islamists expel Fatah from the Gaza Strip.
The Gaza-born politician was expelled from Fatah in 2011 over allegations of financial corruption and murder, and his name draws both loathing and admiration on the Palestinian street.
Despite his exile, Dahlan - with his meticulously coiffed hair and his immaculate suits - still has an important support base among Palestinians and has repeatedly accused Abbas of using "political verdicts" against him.