Hamas sources confirmed al-Ismary was a member of the movement`s military wing, the Ezzedine al-Qassam Brigades.
The Israeli army said in a statement that a routine patrol on the Israeli side of the border came under attack from snipers in the southern Gaza Strip and that forces responded with fire from the ground and the air.
A military spokeswoman declined to comment on any Israeli casualties in the clash.
The clash is the latest in a handful incidents in recent weeks since a 50-day war ended in Gaza in August.
On Friday, Israeli planes bombed a Hamas militant base in the Gaza Strip in response to a rocket that militants launched earlier that day.
Israel launched its Gaza offensive on July 8 with the declared aim of halting cross-border rocket salvoes by Hamas. The fighting was ended by an Egyptian-brokered truce on Aug. 26.
More than 2,100 Palestinians, most of them civilians, were killed in seven weeks of fighting, according to the Gaza Health Ministry. Sixty-seven Israeli soldiers and six civilians in Israel were killed.
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