Palestine`s health ministry says 24 Palestinians have been killed in the Gaza Strip where the Israeli military is targeting members of the Palestinian group Islamic Jihad.
Six children and several PIJ fighters - including leader Tayseer Jabari - are among the dead.
Some 300 Palestinian rockets and mortars have been fired at Israel since Friday, an Israeli official said.
Israel says it launched the operations due to "immediate threat" from PIJ.
The latest violence is the most serious flare-up between Israel and Gaza since an 11-day conflict in May 2021 left more than 200 Palestinians and a dozen Israelis dead.
The Israeli military is warning this latest operation - codenamed Breaking Dawn - could last for a week.
As well as air strikes on Gaza, some 19 members of PIJ have been arrested in raids across the occupied West Bank, according to Israel.
Sirens warning of incoming missiles continued to sound in Israeli towns on Saturday, amid more reports of air strikes in Gaza.
Gaza`s health ministry blamed "Israeli aggression" for the deaths of Palestinians, and for the 203 people wounded.
But so far Hamas, the biggest militant group in the area - which has similar ideology to Islamic Jihad and often coordinates its actions with it - does not seem to be firing from its large rocket arsenal.
As a result, there are no reports of Israeli air strikes targeting Hamas, which would mark an escalation in the violence.
Hamas issued strong statements on Friday night saying that "resistance groups" were united. But because it governs Gaza it has its own practical considerations which may stop it from getting more involved.
The calculations of Hamas could change, if for example the civilian death toll in Gaza rises rapidly.
If it does decide to join the fighting then it would quickly get much more intense.
Life in the Palestinian territory has already become much harder in the past week, after Israel closed its crossings with Gaza amid fears that Islamic Jihad would retaliate for the arrest of one of its leaders in the northern West Bank.
On Saturday, Gaza`s only power station closed down because it had not received any fuel deliveries, an electricity company spokesman said.
Of the almost 300 rockets and mortars reportedly fired from Gaza towards Israel overnight, an Israeli official said some 70 did not reach Israeli territory and landed in the Gaza Strip.
The vast majority of those that reached Israeli air space were intercepted by its Iron Dome missile defence system, with no Israeli casualties, officials said.
Some 30 Islamic Jihad targets have been struck, among them two weapon storage facilities and six rocket manufacturing sites, the Israeli Defence Forces (IDF) said. The strikes have injured more than 120 people, Palestinian health officials say.
Referring to the initial strike on Friday, Israeli Prime Minister Yair Lapid said Israel carried out "a precise counter-terror operation against an immediate threat".
The IDF said its attacks targeted sites linked to PIJ, including the high-rise Palestine Tower in Gaza City which was hit on Friday in a loud explosion which left smoke pouring from the building.
