Hamas, whose gunmen seized the Gaza Strip by force last June, immediately welcomed the offer delivered by Abbas during a televised speech.
Abbas gave no details about his proposal, including whether he would personally take part in talks or would seek mediation by Arab states. It also was not clear from his wording whether he had dropped all preconditions.
If Abbas were to start negotiating with Hamas, he could jeopardize the broad international support that he gained after Hamas seized Gaza in five days of fighting with Abbas' security forces. The West hoped its backing would lead the moderate Abbas to a peace deal with Israel.
But the Palestinian president has engaged in months of peace talks with Israel that have yielded no tangible results. Earlier Wednesday, Abbas' chief negotiator said it would take "a miracle" to meet the year-end target for a deal set by President Bush.
A close Abbas aide, Nimer Hamad, said circumstances dictate that the Palestinian factions resume dialogue.
"The failure of the peace process, the tragic situation in Gaza, the entire Palestinian situation require thinking courageously of an exit," Hamad said. "We hope that Hamas will respond positively to the call."
In Gaza, Hamas spokesman Taher Nunu greeted Abbas' offer with warmth. "We welcome this call by the President Abbas to launch a national dialogue, and we consider it a positive step," he said.
Abbas' speech started off by criticizing Israel for continued construction in West Bank settlements and other acts that he said dampened peace hopes.
Then he called for a new "national dialogue" among Palestinians that could "end the internal division that harms our people, (our) cause."
Abbas said if talks succeed, "I will call for new legislative and presidential elections." Abbas won a presidential ballot to succeed Yasser Arafat, who died in 2004, but Hamas swept Abbas' Fatah movement out of power in 2006 parliamentary elections.
Over the past year there have been several efforts, notably by Egypt and later by Yemen, to repair the rift between the rivals, but to no avail.
The lack of apparent progress in peace talks with Israel has troubled the Palestinian leader.
This week, he had a particularly tense meeting with Israeli Prime Minister Ehud Olmert. The leaders spent much of the time complaining - Abbas about construction in Israeli settlements, Olmert about Palestinian attempts to keep the European Union from granting Israel closer ties.
The internal Palestinian divisions have weakened Abbas' negotiating position, and Israel has said no peace deal can be implemented as long as Hamas rules Gaza.
Hamas has persistently rejected demands by the West that it recognize the Jewish state, renounce violence and accept previous peace deals. Since Israel's withdrawal from Gaza in 2005, Hamas and other militant groups have stepped up rocket attacks on Israeli border communities.
Israel and Abbas' administration restarted peace talks at a U.S.-hosted summit in November and set a year-end target for reaching an agreement.
The lead Palestinian negotiator, Ahmed Qureia, said Wednesday it is increasingly unlikely the sides can meet their jointly stated goal.
Speaking at a Fatah meeting, Qureia said negotiating teams were working on all key issues of the conflict, including the borders between Israel and a future Palestinian state, the fate of millions of Palestinian refugees and the final status of Jerusalem.
But "gaps still exist," he said. "If we continue in negotiations, progress can be made, but not final progress. I don't think that we can reach an agreement this year unless there is a miracle."
Israeli officials have said a framework agreement, as opposed to a final deal, was the most likely outcome of the talks. A growing corruption probe that threatens to topple Olmert has cast further doubts on peace prospects.