Tel Aviv says its action was in response to rockets launched by Hamas over the weekend.
Israeli military aircraft have struck a series of targets in the besieged Gaza in response to rockets launched out of the Hamas-ruled territory.
It was the third consecutive night of fighting between the two sides.
Israel's military said it attacked a number of alleged Hamas targets early on Monday. There were no reports of casualties on either side.
Israel has blockaded Gaza for more than a decade, making it difficult for Palestinians to run their businesses.
A strict control over what can be imported into Gaza means there's a shortage parts and equipment needed to run much-needed machines.
Recent tensions were heightened following last week's escape from an Israeli prison by six Palestinian inmates, four of whom have been caught, as well as struggling efforts by Egypt to broker a long-term cease-fire in the wake of an 11-day war last May.
The UN High Commissioner for Human Rights said in late May that Israeli air strikes on the territory had resulted in "the widespread destruction of civilian infrastructure".
Israel's foreign minister on Sunday proposed improving living conditions in Gaza in exchange for calm, aiming to solve "never-ending rounds of violence" as the two sides exchanged fresh fire over the weekend.
The Israeli military said three separate rockets were launched from blockaded Gaze on late Sunday and early Monday, saying at least two of them were intercepted by its rocket defences.
A Gaza deal to disempower Hamas
The plan, which includes infrastructure and employment benefits, aims to convince Palestinians in the enclave blockaded by Gaza that it is Hamas's fault that " they live in conditions of poverty, scarcity, violence and high unemployment, without hope", Yair Lapid said on Sunday.
Lapid's plan does not yet amount to official policy in Israel's eight-party coalition government but has support from Prime Minister Naftali Bennett.
In the first stage of the plan, the infrastructure in Gaza would receive a sorely needed upgrade – from electricity to transport.
"In exchange, Hamas will commit to long-term quiet," he added.
"It won't happen without the support and involvement of our Egyptian partners and without their ability to talk to everyone involved," Lapid said.
"Any breach by Hamas will stop the process or set it back," he warned.
In the second stage, Gaza would see the construction of an artificial island off its coast that would allow the construction of a port, and a "transportation link" between Gaza and the West Bank would be created.
Lapid said he had presented the plan to "partners in the Arab world," as well as to the United States, Russia and the European Union.
"There is still work to do, we're still on the drawing board, but if this plan has a chance to succeed and gains widespread support, I'll propose it to the government as the official position," he said.
Just hours after Lapid's remarks, renewed violence flared.
Meanwhile, Egyptian-mediated efforts to deliver a long-term truce have struggled with the sides unable to agree on a system to renew Qatari payments to needy Gaza families.
Israel has demanded guarantees that Hamas does not divert the money for military use.
Gaza is an impoverished territory whose population is overwhelmingly comprised of families who fled or were forced from properties in what is now Israel during the war surrounding Israel's establishment in 1948.
Palestinians have long pushed for Israel to end a crippling blockade that has devastated Gaza's economy, while Israel is demanding that Hamas free two captive Israeli civilians and return the remains of two dead Israeli soldiers.
Hamas has been in control of Gaza since ousting the forces of the internationally recognised Palestinian Authority in 2007, a year after the group won Palestinian parliamentary elections.
Since then, Israel and Hamas have fought four wars and numerous smaller rounds of fighting.