"We will strike Hamas everywhere -- in Gaza, in Damascus -- in order to avoid the assassinations of Israelis," Prime Minister Ariel Sharon's chief spokesman Raanan Gissin told AFP.
"This organisation does not want to negotiate but destroy the state of Irasel and kill Jews."
The attack was Israel's first major response to a double Hamas suicide bombing in the southern city of Beersheva last week which left 16 Israelis dead, as well as the two bombers.
Gissin said the possibliity of an attack on the field used as a training ground for members of Hamas' military wing had been studied for some time.
"Before we hit this football pitch we watched for a few weeks in order to wait for the right moment to strike," he said.
"It was not a football field but a killing field where they were training in the use of explosives and attacks against Israelis."
Israel has been painting parallels between its fight against Palestinian militants and Russia's battle with Chechen rebels in the wake of last week's hostage drama at a school in the town of Breslan which left more than 300 people dead.
"If you want a justification of our action yesterday, switch on your television set and watch the pictures from Beslan. We won't allow this horror to happen here."