Abbas met Hamas leaders on Saturday night for the first time since the group routed his long-ruling Fatah in 25 January, parliamentary elections.
In the meeting, Abbas did not demand the group recognise Israel or Palestinian-Israeli accords if it wants to form the next government, a Hamas leader said.
Abbas, who was elected separately last year and wants to restart peace talks with Israel, must now work out a power-sharing arrangement with the group.
Israel's Channel 1 TV reported that Abbas sought to maintain control of Palestinian police in the meeting, but Ismail Haniyeh, a Hamas leader, said no such demands were made.
Haniyeh told reporters after the meeting: "There is no truth to baseless reports that President Abbas wants to take over the security institutions."
Abbas, who did not comment, has not said he wants to retain authority over the 58,000-member Palestinian police. But other senior Fatah officials have insisted that Fatah-dominated security forces would not submit to Hamas control.
Honour deals with Israel
Abbas, who says he plans to stay on as president, has said he intends to ask the new cabinet to honour the Palestinian Authority's previous deals with Israel.
Asked if any conditions were imposed on Hamas, Nabil Abu Rdeneh, an Abbas aide, said: "It's natural that the incoming government must be in harmony" with Palestinian commitments.
Hamas leaders continue to refuse
to recognise Israel
Hamas leaders said Abbas did not demand they recognise Israel or honour agreements with Israel.
The Palestinian president "did not pose any political conditions related to the agreements, or to anything else," Haniyeh said.
Asked if Hamas would honour past deals with Israel, he said: "The Israeli occupation has to recognise our legitimate rights first. Negotiations with Israel, are not on our agenda."
As for recognising Israel, Mahmoud Zahar, another Hamas leader, said: "We are not going to recognise the Israeli enemy."
Abu Rdeneh and Haniyeh said the new, Hamas-dominated parliament would convene for its first session on 16 February.
If Israel does not let Hamas lawmakers from Gaza travel through Israel to the seat of the Palestinian government in the West Bank town of Ram Allah, then the group will use video-conferencing to include them in the deliberations, Haniyeh said.
With Saturday's meeting, unofficial consultations on forming a new government have begun, Haniyeh said.
After parliament meets on 16 February, Hamas will nominate a prime minister and submit that name to Abbas, who would then formally charge the nominee with forming a government, he added.
"The Israeli occupation has to recognise our legitimate rights first. Negotiations with Israel, are not on our agenda"
a Hamas leader
Although Abbas has not yet chosen Hamas for that job, Abu Rdeneh said that as the biggest bloc in parliament, it will be the group's right to form the cabinet.
Zahar predicted a Hamas-led government would be in place by the end of February, and Haniyeh said it would be made up of politicians from various parties and technocrats.
Deal with Fatah
Hamas, a novice to national politics, has invited Fatah to join a governing coalition, but has not received an official answer, Haniyeh said.
An alliance with Fatah would allow Hamas to sidestep dealings with Israel, which the Palestinians cannot avoid entirely, if only for economic reasons. The Palestinian infrastructure is heavily intertwined with Israel's, and most Palestinian imports pass through Israeli-controlled borders.