The officer said that the army was investigating why reinforcements were not sent to back up the Givati troops and whether the soldiers were sent on the correct path.
The IDF said that the clashes occurred near Kibbutz Be'eri, in the western Negev, as troops entered the Strip to arrest a band of suspicious looking figures.
The soldiers were killed after troops spotted two Hamas militants planting a bomb near the Israeli border. Troops pursued the militants, only to fall into an ambush by another Hamas force lying in wait, Israeli defense officials said.
Three other soldiers were wounded in the clashes, two of them moderately, and were taken to the Soroka Medical Center in Be'er Sheva for treatment.
The army named one of the slain soldiers as Corporal Matan Ovadati, 19, of Moshav Patish. The names of the other fatalities have not yet been released.
An IDF spokeswoman said soldiers had shot several Palestinian gunmen during the fighting, though there were no reports of injuries among the militants.
The six Israeli casualties were struck in the first few minutes of the clashes. Two were killed instantly, another was critically wounded, and the other four sustained various levels of injuries.
Palestinian medical workers and Hamas reported that IDF troops killed four Hamas gunmen in a separate battle in Gaza near a terminal used to supply fuel to the coastal territory.
Hamas said soldiers, backed by helicopters, killed the four militants during fighting east of Gaza City, a few hundred metres from the Nahal Oz border terminal. The terminal was the site of a terrorist attack last week, in which two Israeli civilian workers were shot dead by Gaza gunmen.
An IDF spokeswoman said soldiers clashed with Palestinian gunmen in the area and identified hitting them. An Israel Air Force air craft also fired at a group of gunmen, the army said.
At least five Palestinians were injured in the clashes at several points in the Gaza Strip, Hamas and medics said.
Two Palestinian civilians were wounded when their house was hit by a tank
shell, medics said. The army did not immediately comment on that incidents.
In one of the areas east of Gaza City, IDF armored vehicles hit and damaged a mosque, local residents said. Orange and olive trees were also
uprooted, the witnesses said. The IDF did not immediately comment on the damage to the mosque and trees.
Throughout the fighting, militants fired 10 Qassam rockets and a number of mortar shells at the western Negev on Wednesday morning. There was no word of casualties in any of the incidents.
Hamas claimed responsibility for both the Qassam fire as well as the slaying of the IDF soldiers.
Meanwhile, an IDF soldier was moderately wounded late Tuesday when shot by a Palestinian sniper in the central Gaza Strip.
Earlier Tuesday evening, the Israel Air Force attacked two Palestinian militants as they rode a motorcycle through the northern Gaza Strip, killing one and wounding the other, Hamas police officials said.
They identified the casualties from the missile attack in Jabalya refugee camp as members of Islamic Jihad, one of several Palestinian militant factions.
The dead man was named as Mohammed Ghausain, Islamic Jihad's commander in northern Gaza. He was hit while riding his motorcycle in the Jabalya refugee camp, Palestinians said.