"We asked him to meet within the coming two days to consult with Hamas, the largest party in the Palestinian legislature, about the shape of the political partnership for the next era and about all the Palestinian people's issues and topics," Ismail Haniyeh, told worshippers at a mosque in a Gaza refugee camp.
Prime Minister Ahmed Qureia and his Cabinet resigned to make room for a Hamas-led government.
Israel will not negotiate with a Palestinian government that includes Hamas, acting Prime Minister Ehud Olmert said Thursday, responding to a sweeping victory by the Islamic militant group in parliament elections.
"The state of Israel will not negotiate with a Palestinian administration if even part of it is an armed terrorist organization calling for the destruction of the state of Israel," he said in a statement.
His comments came after a three-hour emergency meeting between Olmert and senior Cabinet ministers, called after it became clear that Hamas had decisively won Wednesday's vote — a result that plunged Mideast peacemaking into turmoil.
But according to a poll, nearly half of Israelis believe Israel should talk to a government led by Hamas. CBS News correspondent Robert Berger reports 48 percent support talks with Hamas while 43 percent are opposed.
The Abbas-Haniyeh meeting would have to take place in Gaza because Haniyeh would not be permitted by Israel to travel to the West Bank, the Palestinians' seat of government.
He spoke a day after official election results gave Hamas 76 seats in the 132-member Palestinian parliament.
Abbas said he would ask Hamas to form the next government.
"Until now, we haven't asked anyone to form the government," Abbas said outside his office. "We are carrying on contacts with all factions, and of course we will ask the party that won the majority to form the government."
Hamas' landslide victory in Palestinian elections unnerved the world, darkening prospects for Mideast peace and ending four decades of rule by the corruption-riddled Fatah Party.
It was the first time ever that militant Islamists have come into power peacefully in a democratic election considered free and fair by international observers, reports CBS News correspondent David Hawkins.
But that doesn't mean it's time for the world community to rejoice, Sen. Joseph Biden, D-Del., said on CBS News' The Early Show.
"One election a democracy doesn't make," he told co-anchor Harry Smith. "That seems to be the mistake we're making throughout the middle east. We seem to think if you hold an election in a Muslim state that all of a sudden you have a democracy. It's far from it."
The parliamentary victory Thursday stunned even Hamas leaders, who mounted a well-organized campaign but have no experience in government. They offered to share power with Abbas, who said he may go around the new government to talk peace with Israel.
"The Palestinian people and the Israeli people, by clear majorities on both sides, want a two-state solution," Biden, who went to the Mideast to observe the election, said.
"All the banners I saw that were read for me by staff who speak Arabic, not a single one mentioned the destruction of Israel. Not a single one talked about the peace process. They talked about corruption. They talked about mismanagement," Biden said. "So the irony is the Palestinian people, at the highest level of wanting to settle with Israel, voted for the worst guys to do the settling."
Mahmoud Zahar, another Hamas leader, said Thursday that Hamas planned to overhaul the government.
"We are going to change every aspect, as regards the economy, as regards industry, as regards agriculture, as regards social aid, as regards health, administration, education," he said.
Some experts believed the Hamas victory would force it to moderate. Others feared it would embolden the group to remake Palestinian life in keeping with its strict interpretation of Islam.
"We don't want the Palestinian people and cause to be isolated. We don't want a theocracy," said independent lawmaker Hanan Ashrawi. "Hamas promises reform, sure they will do that, I would like to see reform. But what worries me is things like legislation on education, culture, social welfare, the ramifications for peace in the future."
Leaders across the world are demanding that Hamas, which is branded a terror group by the U.S. and European Union, renounce violence and recognize Israel.
Biden called for cutting off U.S. and other international aid to the Palestinians.
"You cannot pour millions and hundreds of millions of dollars into a group that, in fact, calls for the destruction of an ally or for any country, for that matter," Biden said on The Early Show.
Hamas knows it isn't like by the world community (audio), reports Hawkins, and may not care if U.S. aid is cut off.
"One Hamas candidate told me, during the campaign, before they won the election, that they're not really worried about the cutoff of financial aid, because they have rich friends in the Arab world," Hawkins said.
However, Hamas leaders immediately took to the international — and even Israeli — airwaves to send out a moderate message.
"Don't be afraid," Haniyeh told the BBC.
Zahar said the group would extend its year-old truce if Israel reciprocates. "If not, then I think we will have no option but to protect our people and our land," he said.
At a victory news conference late Thursday, however, Haniyeh said Hamas will "complete the liberation of other parts of Palestine." He did not say which territories he was referring to or how he would go about it.
Hamas has largely adhered to the cease-fire declared last February, while a smaller militant group, Islamic Jihad, carried out six suicide bombings against Israelis during that period.
Abbas said he remained committed to peace talks and suggested they be conducted through the Palestine Liberation Organization rather than the Palestinian Authority. That could help him sidestep a Hamas-run government in peace talks.
"I am committed to implementing the program on which you elected me a year ago," he said in a televised speech. "It is a program based on negotiations and peaceful settlement with Israel."
Hamas' victory was cheered in the Arab world, though many said they feared the group would become even more radical under pressure from its hard-line backers, Syria and Iran.
The rise of Hamas is certain to be a key issue in Israel's March 28 election.