The agreement reached in the Saudi city of Mecca on February 8 had halted weeks of bloody factional fighting in which more than 90 people were killed in the Gaza Strip.
Hamas accused Fatah of ambushing his car. Abdel-Halim Awad, a Fatah spokesman, said Hamas fighters had fired first on a car carrying members of the al-Aqsa Martyrs Brigades, a group which is linked to the Fatah faction.
Fighting quickly spread in Beit Hanoun as Hamas forces attacked a Fatah office and a separate security complex.
Later on Sunday witnesses heard gunfire in Gaza City, and a number of injuries were reported.
Fatah later denied any involvement in the shooting of al-Kafarna and a statement from Hamas only said he was killed by "suspect fire".
Fatah security forces declared a high alert in northern Gaza, ordering their men to reinforce their positions and set up checkpoints to intercept Hamas vehicles.
Tension had risen on Saturday after Fatah gunmen shot at the convoy of a Hamas cabinet minister in the occupied West Bank, and armed men stormed the al-Quds University in Gaza City, wounding a Fatah student council member.
Haniya said in a television interview that the unity government would be unveiled on Wednesday or Thursday and a parliamentary confidence vote would be sought on Saturday.
He said differences over who would hold the powerful post of interior minister, with control over security forces, were close to being resolved, but gave no details.
Haniya said he planned to travel with Mahmoud Abbas, the Fatah-aligned Palestinian presiden, to an Arab summit in Saudi Arabia aimed at reviving an Arab initiative for peace with Israel first launched by the host country in 2002.
|"We have agreed to finalise the national unity government and we will go to the summit with the government in place and, as president and prime minister"|
Ismail Haniya, Palestinian prime minister designate
Haniya said: "We have agreed to finalise the national unity government and we will go to the summit with the government in place and, as president and prime minister, we will ask the Arab countries to support [the new administration]."
The Saudi plan offered Israel peace with all Arab countries if it relinquished land it occupied in the Middle East war in 1967 and allowed the creation of an independent Palestinian state.
If Abbas and Haniya both travel to Saudi Arabia it will be the first time they have appeared together on the international stage. In Mecca last month they each headed rival groups.
Abbas was due to meet Ehud Olmert, the Israeli prime minister, in Jerusalem later on Sunday, but little progress was expected.
Israeli officials said Olmert would reiterate that Israel would keep up its boycott of any new Palestinian government unless it recognises the Jewish state, renounces violence and accepts past peace deals as demanded by the United States and its partners in a quartet of Middle East mediators.
The unity government agreement falls short of these demands.