Major-General Yoav Galant, the head of the army's southern command, has ordered the appointment of a senior officer "to investigate all aspects of this incident and to present findings within 48 hours", the statement said.
Mark Regev, an Israeli government spokesman, told Al Jazeera on Tuesday that an investigation had to be "done professionally and seriously".
"It's very easy to jump to conclusions and one has to be cautious. At this stage, no one knows exactly what happened, except for the fact that this was a zone where there was conflict," he said.
"Anyone who thinks that Israel deliberately targeted Palestinian civilians - that is simply not true. We do not see the Palestinian civilian population as our enemy; on the contrary."
B'Tselem, an Israeli human rights group, has also launched an investigation into the incident.
It has called on the Israeli military to release footage from the drone that fired the missile that caused the explosion.
Regev's admission that Israel has not reached a full conclusion on the incident contrasts with an earlier denial by the Israeli army that one of its own missiles caused the deaths.
Israel had said on Monday that the explosion took place after an air raid hit two Islamic Jihad fighters carrying sacks of explosives towards a battle between Israeli troops and Palestinian fighters nearby.
|The events in Gaza are threatening|
efforts to forge a ceasefire [AFP]
"Initial checking shows very conclusively that we are talking about two militants who were very close to the house. Those militants carry on them a very large amount of explosives," Captain Avital Leibowitz, an Israeli army spokesperson, told Al Jazeera.
"We targeted those militants since they were a threat to our forces. As a result there was a very large explosion. That explosion actually caused the destruction of the house and unfortunately the tragic event of those dead Palestinians."
But David Chater, Al Jazeera's correspondent reporting from the scene on Tuesday, said another account of what happened contrasted with Israel's version of events.
Ahmed Abu Megteg, whose children and wife were killed in the explosion, told Al Jazeera there was no fighting in the area.
"I did not see any fighters, There were no fighters around here ... no fighting, neither from the Arabs or the Israelis," he said.
Reports suggest that the explosion was caused by a missile from an Israeli drone, targeting an unarmed fighter who had moved to stand outside the house.
Chater said there appeared to have been two missiles fired from the drone.
The first missile targeted four fighters, armed with a Kalashnikov rifle and carrying a bag containing rocket-propelled grenades.
He said the men had put the bag down and the grenades were later recovered, intact, by B'Tselem.
"It [the bag] did not explode. There was no secondary explosion as the Israeli military are saying.
"Three men out of the four were injured by that first missile attack ... the fourth one, unarmed, walked down the street," he said.
"He was killed by a second blast and that second blast from the drone caused the deaths of the mother and her four children."
Ehud Olmert, the Israeli prime minister, said on Tuesday that Israel "deeply" regreted the deaths.
"The state of Israel and the government deeply regret that civilians not involved [in the violence] are affected and even more so when it concerns a mother and her four children," he said in a weekly cabinet meeting.
But he also criticised Hamas for operating in civilian areas.
The events in Gaza threaten Egyptian efforts to forge a ceasefire between Israel and Hamas and end violence that is endagering US-brokered talks on Palestinian statehood.
"This aggression does not serve efforts being exerted to achieve calm, and it obstructs the peace process," Mahmoud Abbas, the Palestinian president, whose Fatah faction controls only the West Bank, said.
Ehud Barak, the Israeli defence minister, said a truce in the Gaza Strip was unlikely as Israel was locked in a showdown with Hamas.
A total of seven Palestinians were killed in the latest Israeli operations in Gaza.
Troops withdrew from Gaza overnight, an army spokeswoman said early on Tuesday.