Abbas dismissed warnings the early polls would lead to civil war between the Palestinians.
"Despite the suffering, the pain, the confrontations whoever is responsible for them, we will not allow ourselves to sink into a civil war," he said. "Palestinian blood will rest a border that will not be crossed."
Abbas expressed determination to keep the Palestinian Liberation Organisation as the only legitimate representative of the Palestinian people.
"Those who talk about the illegitimacy of the PLO’s executive committee are operating under its umbrella abroad."
The governing Hamas movement immediately rejected Abbas's announcement.
It denounced Abbas' decision as "coup" against the will of the Palestinian people and some of its leaders, including Mahmoud Zahar, the foreign minister, called on him to resign.
Wasfi Kabha, the minister of prisoners affairs, said: "Our priority is to form a national unity government. It is the only solution. We reject anything which complicates the Palestinian situation."
Hamas, which surprised Fatah to win parliamentary elections in January, had earlier said it would regard any call for fresh elections as a coup.
A senior aide to Abbas said on Saturday that early elections could be held until the middle of next year for legal and technical reasons.
Saeb Erekat said Abbas first had to issue a presidential decree covering the early parliamentary and presidential polls. After that, voter rolls would need 90 days to be updated.
"Technically, the elections cannot be held before mid-2007," Erekat told Reuters.
In the West Bank city of Nablus, hundreds of supporters of Abbas' Fatah movement rushed into the street in celebration, with dozens of gunmen firing in the air.
In Gaza City, dozens of Fatah loyalists and members of his Presidential Guard gathered outside his residence, firing weapons in the air in celebration and chanting: «We are ready to redeem you with our souls and blood, Abu Mazen.»
Hamas has called a demonstration after sunset prayers in Gaza City to condemn the call for early elections.