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.