The postponement should not be more than three months, Salim al-Zanoon, head of the Palestinian National Council, told reporters, with key members of the Palestinian leadership calling for more time to prepare.
The meeting of the Palestine National Council (PNC), a congress representing those in the Palestinian territories and the diaspora, was to take place on September 14-15.
The PNC serves as the parliament of the Palestine Liberation Organisation.
His resignation along with a number of others from the 18-member executive committee will only take effect with a meeting of the PNC, which includes more than 700 people.
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He remains president of the Palestinian Authority and leader of his Fatah party.
Abbas's allies say his recent moves are part of efforts to inject new blood in the Palestinian leadership.
Critics however argue that Abbas is manoeuvring to empower his allies and marginalise opponents ahead of the 80-year-old's eventual retirement.
Hamas, the Islamist movement that runs the Gaza Strip, and Fatah meanwhile remain deeply divided.
Hamas chief Khaled Meshaal earlier this week said the congress should be postponed until a compromise is struck.
Meshaal, speaking in Qatar where he lives in exile, said Palestinian leaders from Hamas and Fatah had to present a unified front.