'As of now, 36 rocket launches were identified from Gaza towards Israel, ' the army wrote on Twitter.
Israeli media reported several residents of Sderot and other border towns were wounded by rocket fire.
A Palestinian was killed in northern Gaza, while at least six were wounded in raids aimed targeting sites across the strip, the Gazan health ministry said.
Miraculously, there were no injuries reported, but the explosion caused damage in both attacks.
"The Hamas terrorist organization is responsible for everything in and out of the Gaza Strip and will bear the consequences for the acts of terror perpetrated against Israeli civilians", the IDF said.
The strikes came after at least two of dozens of rockets launched from the coastal enclave hit the Israeli town of Sderot, near Gaza's northern border, police and the army said.
It said the Palestinian "resistance" had fired a large number of projectiles at "enemy positions in the Gaza envelope".
Jamie McGoldrick, the United Nations' humanitarian coordinator for the Palestinian territories, in a news release called Israel's restriction of fuel imports "a unsafe practice, with grave consequences on the rights of people in Gaza".
Two homes in Sderot were also reportedly hit by the shrapnel and several cars were damaged.
No group has taken responsibility for the attacks thus far, but Israel is holding Hamas responsible, as it has maintained sole control over the enclave since 2007.
Israeli forces have launched three military assaults on the Gaza Strip since 2008.
The escalation comes after the Hamas leadership convened for a rare meeting in Gaza on Friday.
The IDF closed several roads near the Gaza border earlier on Wednesday after warning it was concerned of a retaliation from Hamas after two of its elite members were killed in an IDF strike on Tuesday.
Deputy Hamas chief in Gaza, Khalil Al-Hayya, told Al Jazeera television: "We can say that actions led by the United Nations and Egypt are in advanced stages and we hope it could yield some good from them". One of the jets struck a factory that was being used to produce components intended for the construction of terrorist tunnels leading into Israel, the army said.
More than 160 Palestinians have been killed by Israeli forces - most during weekly protests at which thousands of Palestinians have expressed their support for the declared right of Palestinian refugees to return to their ancestral homes in what is now Israel.
In an earlier statement, the Israeli military said gunmen had fired on its soldiers from a Hamas post, which was shelled by a tank in response.