The Al-Aqsa Martyrs Brigades, the armed wing of Fatah, made the call after a series of weekend demonstrations in which Fatah’s supporters stormed the Palestinian parliamentary building.
“We ask the central committee to resign immediately and announce an emergency committee,” said Al-Aqsa spokesman, Abu Mohammed.
The call was backed by local Fatah leaders in the southern Gaza strip town of Rafah who had earlier announced their resignation, expecting other leaders to follow suit.
Threat to kill militants
Israel has stepped up its tough talk against Hamas, threatening to liquidate militants if attacks on Israeli targets resume.
Officials have also threatened to withhold tens of millions of dollars in aid unless Hamas disarms and renounces violence.
Hamas has claimed responsibility for scores of suicide attacks in which hundreds of Israelis have been killed.
Israel’s interim Prime Minister, Ehud Olmert, has told Cabinet he had received international support for a tough stance against Hamas.
“We clarified that without a clear abandonment of the path of terror, a recognition of Israel’s right to exist in security and peace, Israel won’t have any contact with the Palestinians,” said Mr Olmert.
“These principles are accepted by the international community. On this issue, I don’t intend to make any compromises.”
Mr Olmert spoke ahead of the arrival of German Chancellor Angela Merkel who will soon visit Israel.
Ms Merkel has warned the European Union would not fund the Palestinian Authority under Hamas if it did not renounce violence.
The EU provides US$606m (A$808m) worth of aid to the Palestinian Authority each year, making it the biggest donor.
Washington has already warned that aid worth US$400m (A$533m) could be cut.
Other key donors such as Japan and Arab states are also reviewing their position.
The Palestinian Authority has long been reliant on international aid.
Hamas defiant
Hamas leader Khaled Mashaal has signaled that it plans to form a Palestinian army including members of its militant wing.
Mr Mashaal has reiterated that Hamas will not recognise Israel.
The claim casts a shadow over international aid to the Palestinian Authority.
Another top Hamas leader, Mahmud al-Zahar, says he doubts that Israel wants peaceful coexistence.
"I think we have a big doubt about Israeli intention," al-Zahar told CNN television's Late Edition program.
He also accused Israel of harbouring expansionist intentions.
Mr al-Zahar set out his demands for peace, including Israel’s withdrawal from areas seized after the 1967 Six Day war, the release of Palestinian detainees and acceptance of a Palestinian state.
But he admitted it could take up to 15 years before Israel’s intentions became clear.
Quartet meets
The so-called Middle East quartet comprising the United States, United Nations, the European Union and Russia, will hold talks in London on Monday to discuss the Hamas victory.
The group working for peace in the Middle East is also expected to consider aid programs to the Palestinians.