Six children and several PIJ fighters – including leaders Khalid Mansour and Taisir Jabari – are among 32 Palestinians reported killed.
An Israeli official said nearly 600 Palestinian rockets and mortars had been fired at Israel since Friday.
Israel says it launched the campaign because of an “immediate threat” from the PIJ.
The latest violence is the most severe flare-up between Israel and Gaza since 11-day conflict killed more than 200 Palestinians and a dozen Israelis in May 2021.
The Israeli military is warning that this latest operation – codenamed Breaking Dawn – could last up to a week.
Palestinian rockets fired from the Gaza Strip on Sunday reached Jerusalem for the first time since the 2021 conflict.
The attacks came after Israel’s senior PIJ leader Khalid Mansour was killed in an airstrike on a house in the Rafa refugee camp in southern Gaza.
The commander had previously survived five assassination attempts by the Israeli military, which accused him of planning terrorist operations out of Gaza.
As well as airstrikes on Gaza, dozens of PIJ members have been arrested in raids in the occupied West Bank, according to Israel, which also states that its forces attacked the PIJ tunnel network.
Gaza’s health ministry blamed “Israeli aggression” for the deaths of Palestinians, and more than 200 people were injured.
Israel accused PIJ militants of mistakenly causing at least some of those deaths – claiming on Saturday that the group killed several children in Jabaliya in the Gaza Strip. The BBC has not been able to independently verify this claim.
By far the region’s largest terrorist group, Hamas – which has a similar ideology to Islamic Jihad and often coordinates its actions with it – does not fire from its large rocket arsenal.
As a result, there are no reports of Israeli air strikes targeting Hamas, which would mark an escalation in violence.
Hamas issued a strong statement saying “resistance groups” are united. But because it rules Gaza, it has practical considerations of its own that may prevent it from becoming more involved.
Hamas’ calculations may change, as the civilian death toll in Gaza rises sharply, for example.
If it decides to join the fight it will quickly become more intense.
Life in the Palestinian territory has already become very difficult, with Israel closing its crossing with Gaza amid fears that Islamic Jihad will retaliate for the arrest of one of its leaders in the northern West Bank.
A spokesman for the power company said Saturday that Gaza’s only power station was shut down because it had not received any fuel delivery.
The US State Department urged all parties to refrain from proceeding – reaffirming its support for Israel’s right to self-defense, noting US concern over reports of civilian casualties, Reuters news agency reports.
In the hope of preventing further violence, Egypt has also stepped in as a mediator between the two sides and reportedly a delegation of officials was sent to Israel on Saturday to act as a mediator.
The latest clash follows Israel’s arrest of Bassem Saadi, who was said to be the head of the PIJ in the West Bank on Monday night.
They were held in the Jenin region as part of an ongoing series of arrests after a wave of attacks by Israeli Arabs and Palestinians killed 17 Israelis and two Ukrainians. Two of the attackers came from the district of Jenin.
The PIJ, one of the strongest terrorist groups operating in Gaza, is backed by Iran and is headquartered in the Syrian capital, Damascus.
It has been responsible for several attacks, including rocket-fire and firing against Israel.
In November 2019, Israel and the PIJ fought a five-day conflict following the Israeli killing of a PIJ commander, which Israel said was planning an imminent attack. The violence killed 34 Palestinians and injured 111, while 63 Israelis required medical treatment.
Israel said 25 of the Palestinians killed were terrorists, including those preparing to launch the rockets.