The attacks were taking place in the southern Gaza town of Khan Younis, about 25 kilometres south of Gaza City.
The warplanes could be heard flying overhead in Gaza City, where smoke from the explosions could be seen in the distance.
In a statement early Friday, the army said it was targeting “terror sites.” It gave no further details.
Palestinian media said a Hamas naval base had been targeted.
There were no immediate reports of injuries.
WATCH: Israeli military aircraft bombed Hamas facilities in the Gaza Strip, hours after two rockets were launched from the Palestinian enclave at Tel Aviv
Palestinian militants in the Gaza Strip fired two rockets toward Tel Aviv late Thursday, the Israeli military said, marking a significant escalation that raised the likelihood of a harsh Israeli reprisal.
The rocket barrage triggered air raid sirens across the city, which is Israel’s densely populated commercial and cultural capital.
No damage or injuries were reported. But it marked the first time that Tel Aviv, some 80 kilometres north of Gaza, has been targeted by rocket fire since a 2014 war with Gaza militants.
Israeli Prime Minister Benjamin Netanyahu rushed to the military headquarters in Tel Aviv and was conferring with senior army officials about a response.
In Gaza, there was no immediate claim of responsibility.
WATCH: Buildings left destroyed in Gaza after 2 rockets launched at Tel Aviv
Brig.-Gen. Ronen Manelis, the Israeli army’s chief spokesman, said officials had no prior warning of the attack and were trying to determine who fired the rockets. Israel holds Gaza’s Hamas rulers responsible for all fire out of the territory.
Tel Aviv Mayor Ron Huldai said he had ordered the city to open public air raid shelters as a protective measure. But he said there were no special instructions and encouraged residents to stick to their daily routines.
“Continue life as usual,” he told Channel 10 TV. “Be calm, but be alert.”
Gaza is controlled by Hamas, an Islamic militant group that seeks Israel’s destruction. Israel and Hamas have fought three wars since Hamas seized control of Gaza in 2007. Hamas possesses a big arsenal of rockets and missiles, but it has sought to contain violence with Israel since the last war in 2014.
Hamas denied responsibility for the attack on Tel Aviv, saying the rockets were launched when the group’s military wing was meeting with Egyptian mediators to try to strengthen a ceasefire between Gaza militants and Israel.
In an unusual step that indicated Hamas was attempting to prevent further escalation, the Hamas Interior Ministry said the rocket fire went “against the national consensus” and promised to take action against the perpetrators.