A senior militant from Islamic Jihad was among more than 15 people killed in Israeli air strikes on the Gaza Strip Friday, prompting the militant group to warn Israel has "started a war".

A child was among those killed in the strikes, the enclave's health ministry said, while Israel's military estimated 15 combatants were killed.

The Israeli army said the strikes were part of an operation "against targets in the Palestinian Islamic Jihad" group.

Islamic Jihad said Israel had "started a war against our people".

"We collectively must defend ourselves and our people. We will not allow the enemy's policy of undermining the resistance and our national perseverance," the group said in a statement.

Flames poured out of a building in Gaza City following an air strike, while wounded Palestinians were evacuated by medics.

Gaza's health ministry reported "a five-year-old girl, targeted by the Israeli occupation" was among those killed.

Islamic Jihad said it was mourning "the great jihadist commander Tayseer al-Jabari 'Abu Mahmud', who was killed in a Zionist assassination in Gaza City".

An Israeli military spokesman said "we are assuming about 15 killed in action" in Gaza, referring to Palestinian combatants.

"We haven't finished yet," spokesman Richard Hecht told journalists.

The strikes come four days after Israel closed its two border crossings with Gaza and restricted the movement of Israeli civilians living near the frontier, citing security concerns.

The measures follow the arrest in the occupied West Bank of two senior members of Islamic Jihad, which has a strong presence in Gaza.

Hamas, the militant group which rules Gaza, said Israel has "committed a new crime for which it must pay the price".

"The resistance in all its military arms and factions is united in this struggle and will speak loudly, as we cannot accept the situation as it is... all fronts must open fire on the enemy," Hamas said in a statement.

Israeli Prime Minister Yair Lapid was due to hold talks with Defence Minister Benny Gantz on Friday evening.

"The Israeli government will not allow terrorist organisations to set the agenda in the Gaza Strip and threaten the citizens of the State of Israel. The security forces will act against the Islamic Jihad terrorists to remove the threat," Lapid said.

Islamic Jihad is blacklisted as a terrorist organisation by the European Union and the United States.

On Friday afternoon, the Israeli military banned large gatherings in communities within 80 kilometres (50 miles) of the Gaza frontier, until Saturday evening.

The measures follow four days of road closures and other restrictions on movement in the border area.

Palestinians including patients and those with Israeli work permits have been prevented from leaving the Gaza Strip since Tuesday, while the goods crossing has also been shut.

Gaza's only power station is at risk of imminent outage due to a lack of fuel supplies through Israel, its manager warned on Thursday.

This week's shutdown of the border area follows a raid by security forces in the northern West Bank district of Jenin.

Israeli forces detained Bassem al-Saadi and another senior member of Islamic Jihad. A 17-year-old member of the group was shot dead by Israeli forces during the raid.