The protest against the party that dominated Palestinian politics for the past 40 years came after President Mahmoud Abbas, who was elected last year to a four-year term, said he would ask the Islamic militant group to form the next government. Abbas later fired six Fatah officials.
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.
Israel's government, caught off guard by the Hamas parliamentary landslide after its vaunted intelligence services predicted a slim victory for Abbas' Fatah Party, said it would have no contacts with a Palestinian government that includes Hamas.
Acting Foreign Minister Tzipi Livni appealed to the international community not to legitimize a Hamas government, saying elections "are not a whitewash for terror," reports CBS News correspondent Robert Berger.
A Hamas-led government could lead to a cutoff of crucial foreign aid to the cash-strapped Palestinian Authority if the Islamic militants do not renounce violence and end their call for the destruction of Israel.
Hamas knows it isn't like by the world community (audio), reports Hawkins, and may not care if U.S. aid is cut off.
Despite international pressure, Hamas leaders said Friday they had no intention of recognizing Israel.
"It's not in our mind now to recognize it as we believe that it's a state that has usurped our land and expelled our people. These issues should be handled before we talk about recognition," deputy Hamas leader Moussa Abu Marzouk said from Damascus, Syria.
Hamas held a celebratory rally in the central Gaza town of Khan Younis, as supporters waved green party flags and caps and chanted slogans.
Small, violent confrontations also broke out in Khan Younis. An argument between roughly 20 Hamas and Fatah loyalists degenerated into gunfire and rock-throwing that left three people injured, one with gunshot wounds. A second gunbattle wounded one police officer and one Hamas supporter, police said.
Wednesday's election exposed deep tensions within Palestinian society and was a clear rebuke to Fatah for its corruption and inability to maintain order in Palestinian towns. Before the vote, veteran Fatah leaders, those most tainted by corruption allegations, resisted repeated calls for reform by the Fatah young guard.
On Friday, thousands of Fatah activists, furious with those leaders for the electoral loss, protested throughout Gaza and the West Bank, demanding the Fatah central committee resign and insisting the party not form a partnership with Hamas. Fatah officials publicly said they would not join a coalition government.
Demonstrators burned cars and shot in the air in front of the Palestinian parliament building in Gaza City. About 1,000 angry party activists went to Abbas' house in Gaza, and hundreds of gunmen fired rifles in the air. Abbas was in the West Bank city of Ramallah at the time.
The protesters then marched through Gaza City toward the security headquarters, tearing down Hamas election posters and banners and burning tires in the street. A small group called on Abbas to resign.
"We are against joining any coalition with Hamas because this means a disaster for Fatah and the Palestinian people," said Samir Mashrawi, a local Fatah leader who was defeated in the election. "Instead, we want to be a strong opposition and we want to fight and end the corruption of some of Fatah's historical leaders."
About 500 Fatah protesters marched through the West Bank city of Hebron, also calling for the resignation of party leaders.
Outgoing Deputy Prime Minister Nabil Shaath defended Abbas as the only hope for salvaging the peace process. "His resignation would lead to either total chaos or to Hamas taking over the presidency as well," he told CNN.
Late Friday, Abbas fired six members of Fatah's Revolutionary Council — a key party organ — who ran against official Fatah candidates in the election. Fatah members who competed against the official party candidates split the Fatah vote in some districts and were blamed for the magnitude of the loss. Fatah also formed a committee to investigate the defeat.
Hamas leader Ismail Haniyeh said he asked Abbas to meet Sunday to discuss forming a government, but Abbas' office said no appointment had been made. Hamas, which has no experience in governing, took 76 of the 132 parliament seats up for grabs.
Ghazi Hamad, one of Hamas' top ideologues, said the group would consider forming a government of technocrats with no connection to Hamas. Such a government might relieve some of the international pressure on the group.
"We want a government for the Palestinian people, and if we couldn't do that then there are lots of options, one of which is a technocrat government," he said.
Hamas, responsible for dozens of suicide bombings on Israelis, has long called for the destruction of the Jewish state. In recent years, some Hamas leaders grudgingly accepted the idea of a Palestinian state in the West Bank and Gaza, but only as a stage toward freeing the rest of Palestine — meaning Israel.
Hamas' unwillingness to change could have a devastating effect on the aid-dependent Palestinian economy, struggling to recover from nearly five years of fighting with Israel.
"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.
Hamas is listed as a terror organization by the United States and the European Union, and Jacob Walles, the U.S. consul-general in Jerusalem, said the U.S. would not give aid to terror organizations, members of terror organizations or ministries controlled by people belonging to terror organizations.
"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
The United States gives $400 million a year to the Palestinian Authority, Walles noted.
"At this point, Hamas has to make a choice. The onus is on them," he said. "If you want to be part of the political process ... you need to recognize Israel, you need to disarm and you need to renounce terror and violence. The choice is theirs."
Former President Jimmy Carter told The Associated Press that the United States is legally bound to cut off funding for a Hamas-led Palestinian Authority. But Carter said Washington should look for other ways to funnel money to the Palestinians, perhaps through U.N. agencies, "so that the people can still continue to have food and shelter and health care and education."
Carter met Friday with Abbas, who told him the Palestinian Authority did not have enough money to pay salaries at the end of the month, even with foreign aid.
If the aid is cut off, "it would create an element of chaos unless the money is made up by other sources," he said. "If the Arab countries come through and the European countries continue to help and maybe Japan, they could continue to operate."
A Palestinian Cabinet minister, speaking on condition of anonymity because of the sensitivity of the topic, said the government would have to fire 30,000 of its 137,000 employees immediately if the aid was cut.
Israeli officials said they will make a decision soon on whether to stop transferring taxes and import duties it collects on behalf of the Palestinian Authority, which make up about two-thirds of the authority's revenue.
But Israelis might not be so willing to shun a Hamas government.
A poll published in the daily Yediot Ahronot on Friday showed 48 percent of Israelis questioned said Israel should negotiate with Hamas, while 43 percent said Israel should not. The poll of 500 people had a 4.5 percentage point margin of error and was conducted Wednesday, before Hamas' victory was announced.