The blasts were so powerful that smoke could be seen in Gaza City, 25 kilometres away from some of the strikes.
The IDF retaliation was immediately followed by more reports of Israeli rocket sirens going off, this time in the Israeli communities close to the Gaza Strip.
The Israeli military said it was targeting "terror sites" in Gaza.
The IDF confirmed that two rockets were fired from the Gaza Strip toward Israel on Thuraday, triggering rocket sirens throughout central Israel.
Air-raid sirens sounded in Tel Aviv on Thursday evening, as two missiles were registered incoming from the Gaza Strip.
That salvo caused no casualties or damage, missing built-up areas.
One of the rockets was reportedly intercepted by Israel's Iron Dome anti-missile system, while the other fell in an open field. There have been several smaller rounds of fighting since, reined in by Egyptian and United Nations mediations.
As of press time, it was not clear who fired the rockets. But another Israeli military spokesman laid the blame with Hamas on Friday.
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That was echoed by US President Donald Trump's special representative for Middle East negotiations, who only minutes after the first reports were issued on Thursday said Hamas was responsible.
Hamas denied involvement, saying the launches took place as its leaders met Egyptian delegates about efforts to secure a long-term ceasefire with Israel.
As well as the strip's rulers, Hamas, other armed factions operate in the territory, including Islamic Jihad, an Iranian-backed organisation that has launched rockets in the past.
The flare-up of Thursday and Friday drew a US statement of support for Israel.
He tweeted, "This is what prevents the world from helping the people of Gaza!" "This method will never work".
While no group claimed responsibility for the attack, Israeli Education Minister and member of security cabinet Naftali Bennett told RT he believes Hamas bears responsibility for the incident anyway. "The time has come to defeat Hamas once and for all", he said on Thursday.
Netanyahu also faced pressure from the centre-left opposition, whose leading candidate, ex-general Benny Gantz, said "only aggressive, harsh action will restore the deterrence that has eroded" under the prime minister's watch.
Since the protests began, one Israeli soldier was shot dead by a Palestinian sniper along the frontier and another was killed during an undercover raid into Gaza.