Israeli warplanes struck militant targets in the Gaza Strip early Thursday after Palestinian rockets hit the Israeli south for the second time in 10 days, sources on both sides said.

Palestinian security sources said the strikes targeted three training bases in Gaza City that were used by Hamas's armed wing, the Ezzedine al-Qassam Brigades, as well as a fourth in the southern city of Khan Yunis.

The raids came several hours after two rockets struck open areas in southern Israel, causing no injuries, in an attack claimed by a small extremist group called "Supporters of the Islamic State in Jerusalem" which recently emerged in Gaza.

It said the attack was to avenge the death of a radical Islamist in Gaza this week who was killed in clashes with the Hamas security forces.

The same group was behind another rocket attack on southern Israel on May 26, which also prompted a series of Israeli air strikes.

The Israeli military confirmed bombing three "terror infrastructure" targets in Gaza overnight in response to the rocket fire, without saying where they were located.

Defence Minister Moshe Yaalon acknowledged that the rockets were likely fired by radical jihadist factions but said Israel held Hamas ultimately responsible.

"Even if those behind the last night's fire were rogue gangs allied with world jihad organisations who are looking to challenge Hamas by shooting at us, we see Hamas as responsible for what is happening in the Strip," he said.

"I suggest you don't test Israel's patience," he said, warning that Israel would not tolerate the return of a reality involving sporadic fire on the south.

"The IDF responded aggressively to the fire and if necessary we will hit back even more harshly, and last summer proved that," Yaalon said, referring to a deadly 50-day war in July and August which left much of Gaza in ruins and some 2,200 Palestinians dead.

- Internal tensions -

Israel has a policy of holding Hamas responsible for every attack launched from territory under its control, no matter which group actually fired.

Israel's public radio said the latest rocket fire was likely related to internal tensions within Gaza which has pitted the territory's Hamas rulers against a handful of small Islamic extremist groups.

The rocket fire came a day after Hamas security officials shot dead an Islamic extremist during a shootout which erupted when they went to arrest him at his home in Gaza City.

Officials identified him as a local leader of a radical Salafist group, although some witnesses said he belonged to a group affiliated with the Islamic State movement.

Salafists are Sunni Muslims who promote a strict lifestyle based on that of early "pious ancestors". In Gaza they have made no secret of their disdain for Hamas over its observance of a tacit ceasefire with Israel and its failure to implement Islamic law.

Since the 2014 summer war, there have been growing signs of internal unrest, with Hamas mounting a tough crackdown on extremist splinter groups.