Israeli air strikes killed two Gaza militants on Monday as they clashed with troops who crossed the border on the eve of a landmark visit by the Qatari emir, medical sources said.

The flareup provoked threats of revenge from the Ezzedine al-Qassam Brigades, the armed wing of the ruling Hamas movement, and a pledge from Israeli Prime Minister Benjamin Netanyahu that there would be no immunity for those firing on the Jewish state.

Two air strikes took place around the northern town of Beit Hanun where militants were firing mortar shells at an Israeli tank and several military vehicles which had crossed the border into Gaza territory, witnesses and security sources said.

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

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

The Qassam Brigades confirmed that the first strike had killed one of its militants and critically wounded another three, naming the dead man as Abderahman Abu Jalaleh, 25, and describing him as a local commander.

The second strike killed a PRC militant whom the group named as Yasser al-Tarabin. The identity of the injured man was not immediately clear.

The Israeli military said 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.

Israeli police said that ahead of the strikes, militants had fired a wave of rockets into southern Israel.

"Four rockets landed in the early hours of the morning," police spokesman Micky Rosenfeld told AFP. "They were fired from the Gaza Strip and landed in open areas, not causing any damage or injuries."

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.

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."

Hamas militants usually observe a de facto truce regarding Israeli targets, but the rare show of force against the military force appeared to be a direct response to the incursion.

"The Zionist enemy continues its crimes and arrogance against our land and people... because of its desire to blow up the situation," the Qassam Brigades said.

"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.

"The real thing we have is rockets. We've got Hamas, supported by Iran, firing rockets at us.. 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 on meeting the Middle East Quartet envoy Tony Blair.

"We're going to prevent them from arming themselves. This is our policy. This is a very different policy that I put in. You don't let them get away with it. And they know that's what we're doing."