Angry activists from the defeated Fatah party of Palestinian Authority leader Mahmoud Abbas have staged rallies in the Gaza Strip, saying he must resign.
Abbas is to hold talks with Hamas soon on the new government
Many gathered outside the parliament in Gaza City, setting fire to government cars and firing shots into the air.
The BBC's Jim Muir in Gaza says they blame the leadership's corruption and inefficiency for Fatah's election defeat to Islamic militants Hamas.
Hamas swept to victory with 76 of the 132 seats in Wednesday's elections.
Mr Abbas said he would ask Hamas to form a new government and Hamas said it would enter talks with Fatah soon to try to forge "unity and partnership".
The comments came as Hamas was facing increasing international pressure to renounce violence against Israel and possibility that foreign donors may withhold millions of dollars in aid to the Palestinians.
Appeal for calm
Protesters outside the legislature in Gaza and thousands more in the refugee camp of Nusayrat called for the entire Fatah leadership to go.
One protester toured the area in a van, telling fellow demonstrators through a loudspeaker: "Fatah lost because of the central committee so we call for them to resign."
The protests against Mr Abbas included those from militant Fatah offshoots like the al-Aqsa Martyrs Brigade.
One militant told AFP news agency: "We call for [Abbas'] resignation from Fatah's revolutionary council and central committee. We want him and his entire team out."
Senior Fatah leader, Mohammad Dahlan, assured the crowd that would not happen, appealing for calm.
There was also violence between Fatah and Hamas supporters in the southern Gaza town of Khan Younis. Several people were injured.
The unrest came as senior Hamas leader Ismail Haniya said Mr Abbas had agreed to meet shortly to start consultations on "a political partnership" and the make-up of the next administration.
Mr Haniya on Friday made his first big speech since the election victory near Gaza City's waterfront.
He told a packed mosque: "When we are calling for unity and partnership it is not because we are afraid or weak or incapable of facing the challenges ahead, but because we believe in unity."
The BBC's Alan Johnston at the mosque in Gaza says an alliance may be necessary for, if Hamas were to try to govern alone, interaction with the outside world might be extremely difficult.
As it is, he says, some Palestinians are concerned that crucial international financial support may be cut back.
On Friday, the European Commission, which offered 280 million euros ($342m) to the Palestinian people last year, admitted it was in a dilemma about funding.
On Friday President George Bush said US aid to the Palestinians would halt unless Hamas dissolved its armed wing and stopped threatening Israel.
Israel has ruled out any talks with Hamas, which it calls "an armed terror organisation that calls for Israel's destruction".
The US, UN, EU and Russia on Thursday urged Hamas to renounce violence and accept Israel's right to exist.
The four powers working for peace in the Middle East will hold talks in London on Monday.
Some of the protesters were from militant offshoots of Fatah
1) Fatah: 55 seats
2) Independent Fatah: 7 seats
3) Independent Islamists: 4
4) Independent Christians: 3
5) Independents: 15 seats
6) Samaritans: 1 seat
7) Others: 1 seat
8): Vacant: 2 seats
1) Hamas - 76 seats
2) Fatah - 43 seats
3) PFLP - 3 seats
4) Badeel - 2 seats
5) Independent Palestine - 2
6) Third Way - 2 seats
7) Independent/other - 4