A Hamas commander has been killed by gunmen in southern
Hussein Shabasi, 28, was shot dead in Khan Younis hours after the truce went into effect at 0300 (0100 GMT).
A Hamas spokesman condemned the killing but refrained from blaming Fatah - led by Palestinian leader Mahmoud Abbas.
The truce between the two factions was agreed on Monday, in an attempt to end fighting in which 30 people have died.
The street battles had intensified in recent days, amid a bitter power struggle between the two sides in
Previous truces between Hamas and Fatah have collapsed, and the BBC's Alan Johnston in
After the killing of Mr Shabasi, Hamas spokesman Fawzi Barhum told AFP news agency: "We do not want to accuse Fatah, but if it turns out that this crime was committed by Fatah members, it will mark a serious violation" of the ceasefire.
Deadlock
Hamas - which won legislative elections a year ago - and Fatah have been trying to form a unity government for many months.
They are deadlocked over Hamas' rejection of international calls on it to renounce violence and recognize
Western donors have been withholding aid, resulting in a deep economic crisis in Palestinian territories.
As the ceasefire came into force overnight, Israeli aircraft bombed a tunnel under the Gaza-Egypt border.
The Israeli military said the tunnel was going to be used by Palestinian militants to attack Israeli targets.
It came one day after a Palestinian bomber from
Photo caption
Palestinian militants in Khan Younis