Mr Abbas condemned Hamas as "murderous terrorists" and "coup plotters", over the group's takeover of Gaza last week.
He was speaking at a meeting of the Palestine Liberation Organisation (PLO), a political group, in the West Bank town of Ramallah.
He ruled out talks with the Islamist group - a rival of his Fatah faction - but said peace talks with Israel should resume despite the crisis, calling on the international community to convene a conference.
Mr Abbas accused Hamas of trying to assassinate him during a planned visit to Gaza a month ago, saying he had seen videotapes in which militants discussed explosives that would be used to kill him.
A Hamas leader in Lebanon, Osama Hamdan, condemned Mr Abbas' speech as "full of lies".
Separately, the European Union has said it will pay EUR22 million (US$30 million) of debt amassed by the Palestinian Authority to strengthen the new government.
External Relations Commissioner Benita Ferrero-Waldner told the European Parliament the EU would also continue humanitarian aid to the region - including to Gaza. The EU is one of the largest donors of aid to the region.
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