Abbas travelled from Gaza City to an undisclosed location for the talks with Hamas leaders Mahmud Zahar and Ismail Haniyah, sources on both sides said.
He was later to hold separate talks later with leaders of Islamic Jihad to ask them to sign up to a mutual ceasefire which he announced with Israeli Prime Minister Ariel Sharon at a breakthrough peace summit on Tuesday.
"We have told Abbas that we will not give up the resistance card for free," Muhammad al-Hindi told Aljazeera on Saturday.
"There are key issues that need to be resolved such as the case of the Palestinian prisoners, halting Israeli aggressions, the separation wall, seizing of Palestinian lands and the building of Jewish settlements."
"Israel has continued provocations against the Palestinian people and no one is blaming it. Meanwhile heavy pressure is being put on the Palestinian resistance. We need to agree on a programme that would help us avoid these pressures," al-Hindi added.
Informal cooling down
Although resistance groups have so far stopped short of fully endorsing Abbas's ceasefire declaration at the Sharm al-Shaikh summit, Hamas leaders insist they are committed to an informal "cooling down" period as agreed with the Palestinian Authority chief.
Shaul Mofaz will meet Muhammad
Dahlan to discuss security issues
"We are in a serious and dangerous time," the former security minister, Muhammad Dahlan, told reporters in Gaza City, saying that the Palestinian factions had "serious responsibility on their shoulders".
Before sitting down with the various groups, Abbas was meeting with the central committee of his dominant Fatah faction, to discuss "recent developments in the political and security arena," Dahlan said.
Dahlan is himself due to hold talks with Israeli Defence Minister Shaul Mofaz to discuss security coordination, an official from Dahlan's office said. It was not clear where the meeting was to take place.
A similar meeting was due to take place Sunday between Palestinian negotiations minister Saib Uraiqat and top Sharon adviser Dov Weisglass. Israel had postponed the talks following Thursday's mortar attacks.
Early on Saturday, Abbas met more than 30 West Bank residents who had been deported to Gaza by Israel, and reassured them that everything was being done to expedite their return home "as soon as possible", an aide said.
Looking ahead to Sunday, Abbas is due to meet the executive committee of the Palestine Liberation Organisation, of which he is chairman. He is also expected to invite all the factions for talks.
In a diplomatic push to maximise the momentum of the Sharm al-Shaikh summit in Egypt, Norwegian Prime Minister Kjell Magne Bondevik is due to arrive in the region on a two-day visit later Saturday, for talks with both Abbas and Sharon.
EU foreign relations commissioner, Benita
Ferrero-Waldner, was also due to meet Palestinian foreign minister Nabil Shaath in Gaza late on Sunday, sources in Shaath's office said.
EU's Benita Ferrero-Waldner (R)
is to meet Nabil Shaath
The EU is one of four sponsors of the internationally drafted roadmap peace plan, which has made little progress since its launch in 2003.
Even though Sharon had promised to release hundreds of Palestinian prisoners, the relevant Israeli committee is to convene on Sunday to debate the list of detainees due for released over the next three months, according to Israeli public radio.
In the first phase of staggered releases, more than 300 prisoners are expected to be freed early next week.
Israel has agreed to the releases as part of a package of goodwill measures, but insists no one with blood on their hands will be included in the deal, contrary to demands from Hamas that all 7500 Palestinian detainees be freed.
Right of return?
Israel will allow the return of 56 Palestinians it deported during West Bank military operations, including the men exiled abroad after holing up in Bethlehem's Church of the Nativity, a senior Palestinian official said on Saturday.
"There was an agreement reached in principle that all Palestinians deported ... will return to their homes," Negotiations Minister Saib Uraiqat told Reuters, saying implementation was expected within two weeks.
"There was an agreement reached in principle that all Palestinians deported ... will return to their homes"
Palestinian Negotiations Minister
Meanwhile, an Israeli mine exploded and wounded four teenagers in southern Lebanon on Saturday, police said, adding that one of the four had to have a leg amputated.
The blast occurred near the Al-Abbad hill, site of an Israeli fortification abandoned in May 2000 when the Israeli army was forced to pull out of south Lebanon because of constant attacks from Hizb Allah.
More than 30 civilians have been killed and hundreds wounded by mines since the pullout, while a score of Lebanese soldiers and UN troops have been wounded during de-mining operations.
The United Nations estimates that the Israelis left some 400,000 anti-personnel mines behind when they pulled out of south Lebanon.