Laila El-Haddad interviews members of armed groups allied to Hamas and to Fatah to discover why they do what they do - read An eye for an eye in Gaza
Late on Tuesday, 20 Hamas and 18 Fatah hostages that had been seized during the days of infighting were released.
"The process of handing over the hostages has been completed," Samih al-Madhoun, a senior leader of Fatah-linked al-Aqsa Martyrs Brigades, said.
The ceasefire had appeared to be holding, bringing people out of their homes for the first time in five days as shops reopened and traffic again clogged Gaza's narrow streets.
The truce took effect after Ismail Haniyeh, the Palestinian prime minister and a senior leader of Hamas, met an aide to Abbas on Monday in a bid to stem a surge of fighting in which at least 30 Palestinians were killed.
Hamas fighters removed their impromptu checkpoints, but some Fatah fighters remained visible in Gaza City, protecting the official residences of Abbas and a senior faction leader as well as the compound of a security service considered loyal to Fatah.
There was a limited police presence in Gaza on Tuesday.
"It is pitiful to witness the bloody scenes in Gaza between the brothers"
Abbas, who is currently in Cairo meeting the Egyptian president Hosni Mubarak, condemned the attack in the Israeli Red Sea resort of Eilat on Monday that killed three people and was carried out by a suicide bomber from Gaza.
"My position regarding this operation is that I do not accept it and I reject and condemn it," Abbas said.
"There was no need at all, and it does not benefit us at all. I do not think that this operation in particular will impact the calm between us and the Israelis in the Gaza Strip."
Speaking after Haniyeh and Abbas met, Mahmoud al-Zahar, the Palestinian foreign minister, said the two sides agreed to hold their fire and remove all their fighters from the streets of Gaza.
The clashes were the fiercest since Hamas beat Fatah in an election last year, leading to an aid embargo being imposed by Western governments.
The violence has derailed unity government talks between Hamas and Fatah. Many shops and schools have been closed.
Previous ceasefires, including one last month, have been short-lived.