The Palestinian militant group Hamas said its fighters had hit back by engaging an armoured Israeli force in southern Gaza on Sunday, and launched two attack drones at military posts on Monday which Israel said were thwarted.
One Israeli soldier was killed during a raid on Sunday, the Israeli military said, but it did not acknowledge an assertion by Hamas that its fighters had destroyed Israeli military equipment during skirmishes.
Israel's military has massed forces near Gaza's border and vowed to wipe out Hamas since the group killed 1400 people and took more than 200 hostages in cross-border raids on October 7.
It has already launched intensive air strikes on Gaza, where at least 4600 people have been killed.
Intensive Israeli air strikes have targeted sites in Rafah and other parts of the Gaza Strip.
Israel said its armed forces' incursions overnight were partly intended to gather intelligence and had helped improve its military readiness but it is not clear when the Middle East's most powerful army might launch a full-scale invasion.
It is also not clear how such an invasion might unfold.
Hamas has built up a powerful arsenal with Iran's help, and Israeli forces would risk be drawn into fighting in a crowded urban setting against a group that has built a vast tunnel network referred to by Israeli troops as the "Gaza Metro".
"During the night there were raids by (Israeli) tank and infantry forces," Israel's chief military spokesman Rear Admiral Daniel Hagari told a briefing.
Describing incursions that went "deep" into Gaza, he said: "These raids are raids that kill squads of terrorists who are preparing for the next stage in the war."
Izz el-Deen al-Qassam Brigades, the armed wing of Hamas, said in a statement on Sunday that its fighters had engaged with an Israeli armoured force east of Khan Younis in southern Gaza.
"Fighters engaged with the infiltrating force, destroying two bulldozers and a tank and forced the force to withdraw, before they returned safely to base," it said.
It said on Monday that it had also targeted two Israeli military posts in southern Israel with drones.
The Israeli military said two drones had been identified crossing from Gaza into Israeli territory and were thwarted.
Analysts say it remains unclear how a full-scale Israeli invasion of the Gaza Strip might unfold.
Israel has said its military campaign will exceed any previous moves against Hamas but the Palestinian group has proved capable of surprising Israel in the past and will be fighting in a dense urban setting with powerful weapons.
Based on what happened in Israeli incursions in 2008 and 2014, Israel's bunker buster bombs and hi-tech Merkava tanks will be up against a vast network of deep tunnels, booby-traps and arms including Russian-made Kornet anti-tank missiles.
