An Israeli air strike on southern Gaza on Wednesday killed a "global jihad" militant who put together a deadly ambush on Israel's border with Egypt, the military said.

The strike targeted a man riding a motorcycle in the southern city of Rafah which lies on the border with Egypt, killing 21-year-old Ghaleb Ermilat, Palestinian medics said. Another person was wounded in the strike.

There was no let-up in rocket fire from Gaza on Wednesday, with at least 10 hitting the Jewish state despite seven Israeli air strikes overnight, police and the military said.

As the violence in and around Gaza entered its third day, Israeli police raised their level of alert in the towns and villages within rocket range, although there were no casualties in the latest strikes.

A previously unknown Islamist group has claimed responsibility for an attack on Israel by militants who crossed from Egypt, according to a video message reported by SITE Intelligence on Tuesday.

The video featured a militant announcing the setting up of a group named the "Mujahideen Shura Council in the Environs of Jerusalem," while other footage showed two gunmen saying they were about to launch the attack, according to the video posted by the US-based monitoring service.

Militants from the armed wing of Gaza's ruling Hamas movement on Tuesday said they had fired 10 Grad rockets at Israel in a rare show of force after Israeli raids killed six.

"This is our answer to the Zionist crimes. It will continue if they carry out more strikes on Gaza," a statement said, with a spokesman confirming it was the first time they had fired such longer-range rockets at Israel since April 2011.

An Israeli air strike killed two Palestinian teenagers near the central Gaza Strip town of Deir el-Balah early on Tuesday, a Palestinian medical official said.

"Two citizens were killed in an Israeli air strike," the official said. "The bodies were only recovered this morning when an ambulance could get to the scene."

France denounced a deadly strike on Israel Monday by militants who had sneaked across the Egyptian border and urged restraint by all parties to prevent a spike in tensions.

An Israeli civilian was killed in the ambush, which sparked a firefight that left at least two gunmen dead. It mirrored a strike in August 2011 in which gunmen from Sinai staged ambushes in southern Israel, killing eight.

Israeli Defense Minister Ehud Barak on Monday blasted Egypt over a "disturbing deterioration" in its security control over the lawless Sinai peninsula after a deadly border attack killed an Israeli civilian.

And he urged Egypt's incoming leadership to "take responsibility" for security in the strife-torn peninsula which shares a 240-kilometer (150-mile) border with Israel.

Israel was still hunting for up to four gunmen who on Monday infiltrated the Egyptian border and staged a deadly ambush, killing one Israeli and sparking a firefight which left two militants dead.

The incident began around 6:00 am (0300 GMT) when a group of up to six gunmen opened fire towards a convoy of vehicles carrying Israeli construction workers to a site where they are building part of the vast border fence, the army said.

Palestinian militants in the Gaza Strip fired eight mortar shells at Israeli troops on the other side of the border fence on Sunday but no soldiers were injured, an Israeli army spokeswoman told Agence France Presse, after two Palestinians were injured by Israeli army fire.

She said that troops returned fire at militants in the central part of the enclave.

The two rockets, apparently fired from Sinai, which landed near towns in the deep south of Israel were linked to the Egyptian presidential election, a senior Israeli security source told AFP on Sunday.

"The rockets fired at Israel over the weekend were a one-off and carried out by those who wanted to influence the Egyptian presidential election," he said referring to militant groups in the Sinai.