Fatah activists have burned cars in an angry protest outside the Palestinian parliament building in Gaza City.
They are demanding the resignation of Fatah leader and Palestinian President Mahmoud Abbas who they blame for the faction's defeat to Hamas in the Palestinian elections.
Mr Abbas has meanwhile confirmed that he will invite the Islamic militant group, Hamas to form a government.
He is expected to meet leaders from the party following Hamas' parliamentary election victory on Wednesday.
But Mr Abaas' Fatah party has said it will have no part in a coalition led by Hamas.
A Fatah spokesman said the militants must now assume full responsibility in the political, security and economic field.
Israel has repeated that it will not hold official talks with Hamas, but says day-to-day contact with the militant group cannot be ruled out.
Earlier, an international diplomatic quartet which is assisting moves towards Middle East peace urged the incoming Palestinian administration to renounce violence and accept Israel's right to exist.
The call came from the US Secretary of State, Condoleezza Rice, UN Secretary General Kofi Annan, Russian Foreign Minister Sergei Lavrov and EU foreign policy chief Javier Solana.
Without naming Hamas, the quartet repeated its view that a two-state solution to the conflict required all participants to renounce violence and terror.
Mr Annan congratulated the Palestinian people on a peaceful election and said the quartet looked forward to working with the new government.
Ahern in call to Hamas
The Minister for Foreign Affairs, Dermot Ahern, has said Hamas must move to renounce violence and recognise the right of Israel to exist in peace and security.
Mr Ahern said he and his EU colleagues are to meet in Brussels on Monday and would need to examine calmly and in cooperation with international partners how best to encourage Hamas to take these steps.
