We do not know if the mainstream Fatah movement will be forced to form a governing coalition with the more radical (and often rejectionist) Hamas movement.
Mr Abbas was much criticised by many Palestinians for remaining on the sidelines of the conflict between the militant Hamas movement and Israel earlier this month in Gaza.
BBC: Palestinian UN vote will hurt peace, says Israel's Regev
The move, officially in honor of the Muslim holiday of Eid al-Adha, was also meant to bolster the reputation of Palestinian Authority President Mahmoud Abbas, whose government is locked in a power struggle with the Hamas movement, which controls the Gaza Strip.
The political leader of the Palestinian Islamist movement Hamas, Khaled Meshaal, does not want to stand for re-election this year, the movement says.
Mrs Merkel has spoken of her commitment to helping resolve the conflict between the Israelis and Palestinians, but the Islamist militant movement Hamas has accused her of ignoring Israeli actions in Gaza.
For instance, they always say that the Fatah movement wants Hamas to recognize Israel.
As the PA's fortunes in the West Bank have waned, those of Hamas, the Islamist movement that runs the Gaza Strip, have waxed.
ECONOMIST: Palestinian unity: Rivals who may need each other | The
Rumours of an impending decision by Hamas, the Palestinian Islamist movement long headquartered in Damascus, to move to Qatar have been strenuously denied but are widely believed.
ECONOMIST: As the turmoil persists, more Syrians are leaving or hiding
Some think Israel may take a new tack with Hamas, encouraging moderates in the movement as it did with Fatah, rather than trying to isolate it, which has strengthened the extremists.
And the United States is interested in getting Damascus to use its influence with Hamas, which Syria views as a legitimate resistance movement and whose leaders take refuge in Syria.
Middle East Professor Avraham Sela says the ceasefire offer shows Hamas is going through the normal evolution of a radical movement.
His Fatah movement, based in the West Bank, is deeply split from Hamas, which governs Gaza.
BBC: Palestinian UN vote will hurt peace, says Israel's Regev
Their movement is controlled by both Israel's blockade of Gaza and by the Hamas government.
"Political bureau chief Khaled Meshaal has notified Hamas's consultative council that he does not wish to be a candidate for the movement's future leadership, " the AFP news agency quoted the statement as saying on Sunday.
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