Since Saturday's surprise assault, Israeli aircraft have been pounding Gaza targets while its ground forces have battled to retake control of border villages and towns overrun by Palestinian gunmen.
Chief military spokesperson Rear-Admiral Daniel Hagari said control of those communities had been re-established but that isolated clashes continued as some gunmen remained active.
"We are now carrying out searches in all of the communities and clearing the area," he said in a televised briefing.
Military officials had previously said that their focus was on securing Israel's side of the border before carrying out any major escalation of the counter-offensive in Gaza.
Hagari said 300,000 reservists have been called up by the military since Saturday, a number suggesting preparations for a possible invasion - though any such plans have not been officially confirmed.
"We have never drafted so many reservists on such a scale," he said. "We are going on the offensive."
Hagari confirmed media reports that 700 people had been killed on Israel's side of the border, including 73 confirmed members of the security forces. He said Israel's military had killed hundreds of Palestinian gunmen.
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