JERUSALEM – Israel on Thursday warned militants in the Gaza Strip not to "test" the Jewish state, as fighter jets pounded targets across the coastal enclave after a Palestinian rocket attack.

Slamming into a house, it was the first rocket to strike Israel's city of Beersheva since the devastating 2008-2009 Gaza war, significantly raising tensions along the enclave's border.

"I don't suggest anyone test the determination of the state of Israel," Prime Minister Benjamin Netanyahu said.

"We are determined to defend our citizens and will not accept anyone bombing our people and our civilians."

Netanyahu's firm warning came after 24 hours of tit-for-tat violence along the border between Israel and the Gaza Strip.

Early Thursday, Israeli jets raided sites across the coastal strip.

Netanyahu said he had ordered the military "to respond with force and they did that immediately on a wide scale."

The military said it targeted several Hamas camps throughout Gaza and a "terrorist squad in the northern Gaza Strip, in the same location where rockets were fired towards the Israeli city of Beersheva."

Later, war planes bombed several other sites across the coastal strip, which the military called "hubs of terror."

On Thursday night, the army said warplanes hit "terrorist targets" in southern and "direct hits were confirmed."

Local rescues services said two people had been wounded in a strike on Rafah, on the Egyptian border.

That would make five Israeli strikes reported by the Palestinians, including three in Gaza City and one in the southern town of Khan Yunis.

There were no reports of casualties in Beersheva, where television footage showed a crater gouged out of a street next to a badly damaged home.

Visiting the city later, Israeli Defence Minister Ehud Barak said the attack on Beersheva was an attempt to "extend" what he called a "permanent conflict" underway on the Gaza border.

Residents of the town said they escaped harm after warning sirens sent them running for the bomb shelters before the rocket struck.

Emergency services raised the alert level in southern Israel and braced for further attacks.

Beersheva, known as the capital of the Negev Desert, is home to about 200,000 people and is 40 kilometres (25 miles) from the Gaza Strip.

The city's deputy major Heftsi Zohar called on the Israeli government and military to "do whatever it takes" to prevent the city from being attacked.

The rocket was fired after clashes along the Gaza border on Wednesday, in which one Islamic Jihad militant was killed and 10 people wounded.

The group said its members were hit as they fired two mortar shells at Israeli tanks operating inside the Gaza Strip.

The Israeli military said an explosive device detonated near a regular patrol along the Gaza border and a mortar shell fired.

"The force spotted several terrorists and opened fire on them, identifying a hit," a spokeswoman said, accusing militants of placing 12 bombs along the border fence in the past two months.

The Ezzedine al-Qassem Brigades, the armed wing of Gaza's ruling Hamas movement, said it participated in attacks against the military, and Israel said it held Hamas "solely responsible" for the flare-up of violence.

Hamas spokesman Ismail Radwan rejected the accusation, blaming the "Zionist enemy" for "this escalation and the targeting of our people."

Israel's Deputy Prime Minister Silvan Shalom described the attack on Beersheva as "a very grave act carried out by the agents of Iran, Hamas."

Israel carried out a massive 22-day offensive in Gaza from December 2008 to January 2009 to stop rocket fire from the coastal enclave.

The offensive killed 1,400 Palestinians, more than half of them civilians, and 13 Israelis, 10 of them soldiers.