This year, Yom Kippur was celebrated on September 24 and 25.
The Israeli military said on Monday evening that it had hit a “military position” belonging to Palestinian militant group Hamas, which controls Gaza.
“The post was located near the area from which assailants carried out a shooting towards [Israeli] soldiers during a violent riot that took place in the Karni area,” it added.
“Additionally, [Israeli] soldiers responded with live fire toward an assailant who fired shots at the soldiers and hit him. No [Israeli] injuries were reported.”
The violence was the latest in series of retaliatory confrontations that have raised questions within Israel as to whether Hamas is seeking to stoke tensions and exploit social divisions, as Israelis reel from the government’s disputed plans for legal reform.
The military also reported on Monday that two suspects who tried to cross into Israel were apprehended by Israeli forces.
The incidents come as Gaza residents have started descending on the heavily guarded Israeli border fence around the enclave, burning tyres, firing towards the fence and throwing homemade bombs.
The riots and resulting clashes have killed several Palestinians.
Israel earlier announced it was beefing up security along the fence in time for Yom Kippur, a day during which activity largely ceases.
There has also been an increase in Gaza militants releasing incendiary balloons across the fence and into Israeli territory, which have been responsible for a large number of crop fires in the agriculturally rich region.
Israel has closed the border with Gaza since September 15, citing security concerns. The decision stops 17,000 Gazans from crossing the border daily into Israel to work.
Many in Israeli security circles say chance to earn higher salaries in Israel are an economic lifeline for the strip’s impoverished residents and a key reason for the relative quiet from Hamas in recent months, which has faced pressure from financially desperate Gazans.