Gaza militants pounded Israel with rockets on Tuesday after six Palestinians were killed and five others injured in a series of air strikes across the coastal strip.

In a rare show of force, militants from the armed wing of the ruling Hamas movement said they had fired at least 10 rockets into Israel and would continue unless the air strikes ended.

Israel police said 45 rockets had hit the Jewish state in a 24-hour period, with one scoring a direct hit on a border police outpost in Yad Mordechai, just north of the Gaza Strip late on Monday evening.

"One border policeman was moderately injured, while another was lightly injured and six others were treated for shock," police spokesman Micky Rosenfeld told AFP.

The sharp increase in rocket fire came in the wake of a warning by Hamas's armed wing, the Ezzedine al-Qassam Brigades, shortly after an afternoon air strike targeted two men on a motorcycle in the central Gaza town of Deir al-Balah, injuring one of them critically.

"This is our answer to the Zionist crimes. It will continue if they carry out more strikes on Gaza," the group said in what was an unusual departure from their customary observance of a tacit truce with Israel.

It was not immediately clear how many of the 45 rockets were fired by Hamas militants.

On Tuesday morning, medics recovered the bodies of two Palestinian teenagers who had been killed in another early-morning air strike in Deir al-Balah.

Their deaths raised to six the number of Palestinians killed in a series of deadly Israeli strikes which began on Monday morning, just hours after gunmen from Sinai carried out an ambush along Israel's southern border with Egypt, killing an Israeli civilian.

Israel has said the sudden spike -- three deadly air raids in just over 12 hours -- was "in no way related" to the border incident, with the military saying the air force was targeting militants about to attack the Jewish state.

The pre-dawn raid killed two 17-year-old youths who were identified as Mohammed Bassem Abu Mealiq and Yusef al-Talbani.

Witnesses said they were trying to cross the fence into Israel, while the army said it had targeted "a terrorist squad handling an explosive device" border.

On Monday, four Palestinians were killed in two Israeli sorties over Beit Hanun in northern Gaza that also wounded three other people, medics said.

One of those killed was 23-year-old Jihad Abu Shebab, an Ezzedine al-Qassam militant, while the second victim, Mohammed al-Zaanin, 25, was not affiliated with any armed faction.

The first strike on Monday killed two Islamic Jihad activists in their 20s, Mohammed Shabat and Ismail Odeh, who were riding a motorcycle near Beit Hanun, medics and witnesses said.

The military said they were part of a "squad of snipers operating near the security fence."

In a separate development, an unexplained explosion in Gaza City killed a two-year-old girl on Tuesday evening, medics said.

An Israeli military spokesman denied there was any air strike in the area at the time.

The last major flare-up in Gaza was in March when four days of tit-for-tat violence left 26 Palestinians dead, and saw militants firing more than 200 rockets into Israel.

The fighting erupted when Israel assassinated a militant leader who it said was responsible for planning an August 2011 attack along Israel's southern border with Egypt in which gunmen sneaked over the frontier and killed eight Israelis.

Within hours, Israel hit back at Gaza, sparking eight days of bloodshed that left 26 Palestinians and an Israeli dead.

Monday's border attack raised fears Israel would once again hold Gaza militants responsible, although there was no such claim in the immediate aftermath of the incident in which an Israeli civilian and two gunmen died.