The "significant upsurge in violence" in the West Bank, in and near Gaza and in east Jerusalem "needs to stop immediately," a spokesman for EU foreign policy chief Josep Borrell said on Monday.

"The firing of rockets from Gaza against civilian populations in Israel is totally unacceptable and feeds escalatory dynamics," the spokesman added in a statement.

The strident call came as Israel carried out deadly air strikes on Gaza following Palestinian militants' rocket fire which Israel said caused no casualties on its side.

The explosive escalation came after days of clashes between Palestinians and Israeli security forces around the Al-Aqsa mosque.

The European Union has been ratcheting up its calls for both sides to step back from the violence.

"The significant upsurge in violence in the occupied West Bank, including in East Jerusalem as well as in and around Gaza needs to stop immediately," it said.

"All leaders have a responsibility to act against extremists. The status quo of the holy sites must be fully respected.

"We reiterate our call on all sides to engage in de-escalatory efforts. Further civilian casualties must be prevented as a priority."