Moreover, Hamas spokesman Fawzi Barhoum said the Israeli atrocities against the Palestinians should not be met with silence. All three died at Malaka, to the east of Gaza City in the north of the Strip.
"A short while ago, terrorists fired at (Israeli) soldiers in the southern Gaza Strip", an army statement said, without mentioning any injuries to the troops. An Israeli officer was wounded in the fresh Gaza flare-up.
There was no immediate confirmation of any rocket fire from Gaza, which typically sets off such sirens, and the military said it appeared to be a "false alarm".
The shooting on the border Wednesday was the second such sniper incident reported by Israel in days.
The IDF attacks came in response to Hamas sniper fire aimed at Israeli forces operating along the security fence on the southern Gaza border, according to the Hebrew-language 0404 military website.
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On Friday an Israeli soldier was shot dead, sparking a fierce wave of bombing that ratcheted up fears of another war.
Gaza-based Palestinian resistance groups have pledged to take revenge for a recent Israeli act of aggression on the blockaded coastal enclave that left three Hamas fighters dead.
That violence was ended late Friday by a UN-brokered ceasefire.
Israel carries out regular attacks on Palestinians in Gaza under the pretext of hitting Hamas targets.