Eleven people have been killed in the air strikes, including a child and PIJ leader Tayseer Jabari.
Israel said the strikes followed an “immediate threat” from the group.
Scores of rockets were fired from Gaza towards Israel overnight, most of them intercepted, Israel’s military said.
The latest violence is the most serious flare-up between Israel and Gaza in just over a year
The 11-day war in May 2021 left more than 200 Palestinians and a dozen Israelis dead before a ceasefire was agreed upon.
Sirens’ warning of incoming missiles continued to sound in Israeli towns on Saturday, amid more reports of air strikes in Gaza that Israel says are targeting PIJ militants.
But so far Hamas, the biggest militant group in the area – which has a 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.
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.
If things stay like this, Egypt – which often acts as a go-between for Israel and Gaza – could have a better chance of brokering some kind of truce.
Cairo officials were preparing on Saturday to host a potential delegation of PIJ representatives as part of that process, Egyptian media said.
Almost 200 rockets were fired from Gaza towards Israel overnight, the Israeli military said. Most were intercepted by the Iron Dome defense, with no Israeli casualties.
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”.
Meanwhile, Interior Minister Ayelet Shaked said: “We don’t know how this will play out… but this could take time… this could be a lengthy round [of conflict] and a hard one.”
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 that left smoke pouring from the building.
The IDF said Tayseer Jabari was a “senior commander” in PIJ and accused him of having committed “multiple terrorist attacks” against Israeli civilians.
Five-year-old Alaa Kaddum was among those killed in the strikes, local officials also said.
In remarks delivered while on a trip to the Iranian capital Tehran, PIJ secretary general Ziyad al-Nakhala said: “We will respond forcefully to this aggression, and there will be a fight in which our people will win.”
“There are no red lines for this battle… and Tel Aviv will be under the rockets of the resistance”.
The latest conflict closely follows Israel’s arrest of Bassem Saadi, reported to be the head of PIJ in the West Bank, on Monday night.
He was held in the Jenin area as part of an ongoing series of arrest operations after a wave of attacks by Israeli Arabs and Palestinians that left 17 Israelis and two Ukrainians dead. Two of the attackers came from the Jenin district.
PIJ, which is one of the strongest militant groups operating in Gaza, is backed by Iran and has its headquarters in the Syrian capital Damascus.
It has been responsible for many attacks, including rocket-fire and shootings against Israel.
In November 2019, Israel and PIJ fought a five-day conflict following the killing by Israel of a PIJ commander who Israel said had been planning an imminent attack. The violence left 34 Palestinians dead and 111 injured, while 63 Israelis needed medical treatment.
Israel said 25 of the Palestinians killed were militants, including those hit preparing to launch rockets.