Doctors in Gaza say there is an increasing reluctance on the part of Palestinians to donate blood.
Donors are staying away because of despair at the factional violence
A surgeon at Gaza City's main hospital said people do not want to see their donated blood shed in the street as Palestinians kill each other.
A ceasefire has largely held since late on Wednesday as gunmen from Fatah and Hamas withdrew from the streets.
The truce came after a week of escalating violence which has brought the territory to a standstill.
Hamas, the largest faction, has rejected calls by Palestinian Authority President Mahmoud Abbas for new elections.
Prime Minister Ismail Haniya, of Hamas, has described Mr Abbas's proposal as "unconstitutional".
The Shifa hospital in Gaza city, the main hospital in the strip, is where many of those killed and injured in the months and years of the conflict with Israel are brought.
Like any hospital in the world, they need blood and blood donors. In the past, that has not been a problem, the BBC's Nick Thorpe says.
There are regular donors and there are those who respond immediately to an appeal.
9 Dec - Mr Abbas suggests early polls; Hamas denounces the idea
11 Dec - Three sons of a Fatah security chief are shot dead on their way to school
14 Dec - Hamas PM Ismail Haniya's convoy comes under fire as he returns from Egypt, killing a bodyguard; Hamas blames Fatah
16 Dec - Mr Abbas says he will call early elections; Hamas calls the move a "coup"
17 Dec - A truce is called after street battles between Hamas and Fatah, but violence continues
19 Dec - Formal truce signed, gunmen begin leaving streets
But as Palestinian fights Palestinian, people have become increasingly reluctant to give blood.
"Nowadays, after - even after appeal - it is a minimal number of people come to donate their blood," Dr Jamaa Saqa, a surgeon at the hospital, explains:
"You ask me why - the answer is that they don't want to give their blood to be shed in the street. They are depressed, frustrated - Palestinian people killing each other. They ask themselves why to give blood?"
In the Intensive Care Department there are eight patients today. Several are victims of the fighting; several simply victims of traffic or household accidents.
With a new ceasefire agreement largely holding, doctors in Gaza dare hope in the future they will have more patients of peace than patients of war, and that the supply of blood will resume, says our correspondent.
Relations between Fatah and Hamas have been poor since Hamas won a shock election victory in January ousting Fatah from power.
But a Western aid boycott imposed because of Hamas's refusal to recognise Israel or renounce violence has helped create a political deadlock.
The groups negotiated over forming a government of national unity but failed to agree terms.
Qassam fire continues
On Thursday, Palestinian militants fired three Qassam rockets towards Israel from the Gaza Strip.
Witnesses and medical sources say one of the rockets hit a house in the town of Beit Hanoun in the Gaza Strip and injured at least three Palestinians.
Another rocket landed in southern Israel without causing any injuries or damage.
There are no reports about the third rocket but the Israeli army says it probably landed in Palestinian territory.
Palestinians militants have broken the ceasefire from last month on several occasions with no casualties in Israel.