"There has been progress in the negotiations with Palestinian factions about ending the militarisation of the intifada," Abbas said after arriving in Qatar on Wednesday on the latest stop of a Gulf tour.
"Intensive discussions are under way with the [Hamas] movement and others with a view to reaching an agreement to calm down the situation," said Abbas, the front-runner to succeed the late Yasir Arafat in elections for Palestinian Authority president on 9 January.
"I am hopeful about [the position of] the Palestinian factions which had agreed to a 53-day truce when I was prime minister [last year], and I hope we will reach an agreement before, or perhaps after, the elections," he added.
Abbas made his remarks as spokesmen for Hamas and Islamic Jihad in the Gaza Strip rejected his argument that the use of weapons since the September 2000 start of the second intifada had been a mistake.
"Such declarations run counter to the consensus among our people over the legitimacy of the resistance," Sami Abu Zuhri, a spokesman for Hamas said. "The problem is the Israeli occupation and not the resistance."
And Muhammad al-Hindi, a leader of Islamic Jihad, said "the Palestinians need weapons of resistance against the Israeli occupation".
In an interview on Tuesday with pan-Arab newspaper Al-Sharq al-Awsat, Abbas said "the use of weapons is harmful and it should stop".
He has previously criticised the "militarisation" of the struggle against occupation but it was his most clear-cut condemnation of the armed factions' tactics since taking the PLO helm after Arafat's recent death.
His willingness to upset the Palestinian groups has won him praise from Israel and its key ally the United States.
"The problem is the Israeli occupation and not the resistance"
Sami Abu Zuhri,
Abbas conceded he had no "guarantees" that armed factions would agree to a truce but said a committee was undertaking daily talks with the groups, who have "some demands that are not impossible [to accommodate]".
"It is normal that all sides should ask Israel to cease all military operations in exchange for a Palestinian truce. This is a universal [Palestinian] condition," he said.
Abbas said the anticipated agreement would also include the Al-Aqsa Martyrs Brigades, an armed offshoot of his Fatah movement.