Israeli jets pounded Hamas positions in Gaza overnight after Palestinians staged a cross-border raid into southern Israel, the military said early yesterday.
The military has said it discovered footprints along its security fence with Gaza on Tuesday and in subsequent searches captured the three who were armed with knives and grenades.
In was the second such breach of the border in recent days.
No injuries or damage were immediately reported.
"We don't know who sent them and what their goal was", an Israeli army spokeswoman told AFP.
The Israeli army was checking reports of the firings and a spokesman declined immediate comment.
Israel's Ambassador to the UN Danny Danon said the latest attempt by the Palestinian Authority to raise its status within the worldwide community and delegitimize Israel is a campaign to "establish facts on the ground by making detours and unilateral moves".
Israel holds Hamas, which rules Gaza, accountable for all attacks launched from the blockaded coastal territory.
"Hamas is at a low point, suffering severe civilian and infrastructure crises", Major General Herzl Halevi said at a conference. The sirens sounded due to machine gun fire that took place inside the Gaza Strip.
Israel fired Iron Dome missiles after mistakenly thinking militants had launched rockets in the Gaza Strip.
On Sunday night, Israel's Iron Dome missile defense system was mistakenly activated along the border with the Gaza Strip.
Hamas has called on Gazans to march to the border with Israel en masse on Friday.