Two Palestinians have been killed in air strikes on the Gaza Strip after they had clashed with Israeli troops crossing into the territory, medical sources say.

Both strikes took place on Sunday around the northern town of Beit Hanoun where fighters were firing mortar shells at an Israeli tank and several military vehicles which had crossed the border, witnesses and security sources said.

The flare-up provoked threats of revenge from the Ezzedine al-Qassam Brigades, the armed wing of the Hamas movement, and a pledge from Israeli Prime Minister Binyamin Netanyahu that there would be no immunity for those firing on Israeli forces.

The first strike hit north of Beit Hanoun, critically wounding four Qassam Brigades fighters, one of whom later died of his injuries, medics and the group said.

As the clashes continued, Israel launched a second air strike east of the town, killing a fighter from the Popular Resistance Committees (PRC) and critically wounding another man, the same sources said.

The Qassam Brigades confirmed that one of its local commanders and a PRC fighter had been killed.

The Israeli military said that both strikes had targeted "a rocket launching squad".

"The squad was targeted in response to mortar shell fire at a routine IDF [army] patrol in the area, near the Israeli kibbutz of Nir Am," a statement said of the first strike. An identical statement was issued following the second strike.

The military refused to say whether troops were operating on the Gaza side of the frontier, saying only "they were near the security fence on a routine patrol".

No damages or injuries were reported from the barrage of rockets that hit southern Israel.

Hamas has recently refrained from violence, and the show of force appeared to be a direct response to the alleged incursion by Israeli tanks.

The Qassam Brigades said in a statement that "the enemy will not be able to tie our hands and his crime will not go unanswered".

Netanyahu also issued a warning of his own.

"We’re not going to let anyone arm themselves and fire rockets on us and think that they can do this with impunity. They’re not going to get away with it," he said.

"The flareup comes on the eve of a high-profile visit by the emir of Qatar to the Gaza Strip, the first such trip by an Arab head of state since Hamas took over the territory in 2007.

(Agencies via Al Jazeera)