Palestinians loyal to political rivals Fatah and Hamas have maintained calm on the streets of Gaza, on the first full day of a formal ceasefire.
Fatah supporters blamed the deaths on Hamas gunmen
The groups withdrew their troops from Gaza's streets on Wednesday morning, despite reports of fresh violence.
Two Fatah policemen were killed hours into the ceasefire, but the group said it would maintain the truce.
The move comes after a week of escalating violence which has brought the territory to a standstill.
Hamas, the largest faction, has rejected calls by Palestinian President Mahmoud Abbas for new elections.
Prime Minister Ismail Haniya, of Hamas, has described Mr Abbas's proposal as "unconstitutional".
There were reports that at least five other Palestinians were injured in the attack that killed the policemen during an overnight patrol.
A Fatah spokesman, Tawfiq Abu Khoussa, blamed Hamas for the killings: "They came under fire from an ambush of masked gunmen affiliated with Hamas," he told the Associated Press.
There was some sporadic violence during the funeral procession
A funeral was held for both men on Wednesday, AP said, with sporadic violence breaking out.
But Fatah insisted it would abide by the ceasefire, with some semblance of normality returning to daily life in Gaza.
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' 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.
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, troops begin leaving streets
Last week bitterness spilled over into violence, with apparent assassination attempts against Hamas Prime Minister Ismail Haniya and Foreign Minister Mahmoud Zahar.
Mr Abbas' call for fresh elections sparked more fighting before the ceasefire was agreed.
Making his first comments on the crisis, Israeli Prime Minister Ehud Olmert said he hoped the ceasefire would hold.
"We are not happy about the developments in the Palestinian Authority," Mr Olmert said.
"Mutual violence between Fatah and Hamas is not something we are happy to see."
Speaking in Jerusalem, he also said he hoped a meeting with Mr Abbas could be arranged in the near future.