Initial exit polls had forecast a slight edge for Fatah, with Hamas coming in a strong second. The polls predicted that neither party would have a majority and would have to rely on smaller parties to form a coalition.
Palestinian pollsters were at a loss to explain the discrepancy between the exit polls. Many voters said they had been afraid to admit to pollsters they had supported Hamas, fearing retribution.
"It's almost like the 1948 U.S. election when supposedly first Dewey won and then Truman," Brookings Institution Senior Fellow Michael O'Hanlon said on CBS News' The Early Show.
A Hamas-only government, without Fatah as a moderating force, is sure to throw Mideast peacemaking into turmoil. The Islamic militants, who carried out dozens of suicide bombings and seek Israel's destruction, have said they oppose peace talks and will not disarm.
"If we look for a silver lining we can see it did not really win because of its terrorism per se," but for the welfare services it has provided for Palestinians, O'Hanlon told Early Show co-anchor Harry Smith. There was also "frustration with the incumbent regime has been so great because it hasn't really delivered."
Ordinary Israelis consider it a bad sign, reports CBS News correspondent Robert Berger.
U.S. election monitors led by former president Jimmy Carter said Thursday the parliamentary elections, the first for Palestinians in 10 years, went well.
"Election day was generally peaceful and the elections thus far appear to be well-administered under the difficult circumstances of ongoing conflict and occupation," said a statement.
The Central Election Commission said the vote count had not been completed. An an official announcement was expected shortly.
Earlier Thursday, top Hamas leader Khaled Mashaal told Abbas his group is ready for a political partnership.
However, Fatah does not want to join a Hamas government, said Fatah legislator Saeb Erekat. "We will be a loyal opposition and rebuild the party," Erekat said, after meeting with Abbas.
Abbas, who favors peace talks with Israel, has said he would resign if he could no longer pursue his agenda.
Israel and the United States have said they would not deal with a government led by Hamas, which has carried out dozens of suicide bombings and which they consider a terrorist group.
"Hamas is a terrorist group. It's on a terrorist list for a reason," President Bush said last May.
And only Wednesday, he said the U.S. won't deal with Hamas unless it renounces violence. The U.S. had been calling for Palestinian democracy. Following the vote, it now faces major new policy decisions, reports CBS News correspondent Peter Maer.
Secretary of State Condoleezza Rice called Palestinian leader Mahmoud Abbas to praise Palestinian democracy and assert that the United States supports him and his policies, Abbas' office said Thursday.
"She asserted to him that U.S. administration will continue supporting the elected president and his policies," said Nabil Abu Rdeneh, an Abbas adviser.