The airstrikes have killed 11 people, including a child and PIJ leader Taiseer Jabri.
Israel said the attacks followed “immediate intimidation” from the group.
The Israeli military said hundreds of millions of rockets were fired from Gaza into Israel overnight, most of which were intercepted.
The latest violence is the most serious flare-up between Israel and Gaza in just over a year
More than 200 Palestinians and a dozen Israelis were killed in an 11-day war in May 2021, before a ceasefire was agreed.
The Israeli military is warning that this latest operation – codenamed Breaking Dawn – could last up to a week.
Sirens warning of incoming missiles continued to sound in Israeli cities on Saturday amid more reports of air strikes in Gaza, which Israel says is targeting PIJ militants.
Palestinian health officials confirmed that one person had died near Khan Younis, in the south of the strip.
But so far Hamas, the region’s largest terrorist group – which has a similar ideology to Islamic Jihad and often coordinates its actions with it – has not been firing from its large rocket arsenal.
As a result, there are no reports of Israeli air strikes targeting Hamas.
Hamas issued a strong statement Friday night 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.
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.
Hamas’ calculations may change, as the civilian death toll in Gaza rises sharply, for example.
It will quickly become more intense if it decides to join the fight.
If things stay that way, Egypt – which often serves as the go-to between Israel and Gaza – may have a better chance of some sort of ceasefire.
Egyptian media said Cairo officials were preparing to host a possible delegation of PIJ representatives on Saturday as part of that process.
Israel-Palestinian conflict explained
The Israeli military said that about 200 rockets were fired from Gaza towards Israel at night. Most were stopped by the Iron Dome defense, with no Israeli casualties.
The IDF said around 30 Islamic Jihad targets had been targeted, two of them weapons storage facilities and six rocket manufacturing sites. At least 78 people have been injured.
Referring to the initial attack on Friday, Israeli Prime Minister Yair Lapid said Israel carried out “a precise counter-terrorism operation against an immediate threat”.
Meanwhile, Interior Minister Aylette Sheik said: “We don’t know how it will go… but it may take time … It can be a long [struggle] and difficult period.”
The IDF said its attacks targeted PIJ-linked sites, including the high-rise Palestine Tower in Gaza City, which was killed in a loud explosion on Friday, sending smoke from the building.
The IDF said Taseer Jabari was a “senior commander” in the PIJ, and accused him of carrying out “multiple terrorist attacks” against Israeli civilians.
Local officials also said five-year-old Ala Kaddum was among those killed in the attack.
In remarks made during a visit to the Iranian capital Tehran, PIJ Secretary General Ziyad al-Nakhla said: “We will respond strongly to this aggression, and there will be a battle in which our people will win.”
“There is no red line for this fight … and Tel Aviv will be under the rocket of the resistance”.
The latest clash comes after Israel’s arrest of Bassem Saadi, said to be the head of the PIJ in the West Bank.
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 Jenin district.
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.