The surprise bombardment shattered a ceasefire in place since January and threatened to fully reignite the 17-month-old war.
Prime Minister Benjamin Netanyahu ordered the strikes after Hamas refused Israeli demands to change the ceasefire agreement.
Officials said the operation was open-ended and was expected to expand. The White House said it had been consulted and voiced support for Israel's actions.
The Israeli military ordered people to evacuate eastern Gaza, including much of the northern town of Beit Hanoun and other communities further south, and head toward the centre of the territory, indicating that Israel could soon launch renewed ground operations.
Israel will, from now on, act against Hamas with increasing military strength, Netanyahu's office said.
The attack during the Muslim holy month of Ramadan could resume a war that has already killed tens of thousands of Palestinians and caused widespread destruction across Gaza.
It also raised questions about the fate of the roughly two dozen Israeli hostages held by Hamas who are believed to still be alive.
A senior Hamas official said Netanyahu's decision to return to war amounts to a death sentence for the remaining hostages.
Izzat al-Risheq accused Netanyahu of launching the strikes to try and save his far-right governing coalition and called on mediators to reveal facts on who broke the truce.
There were no reports of any attacks by Hamas several hours after the bombardment, indicating it still hoped to restore the truce.
The strikes came as Netanyahu comes under mounting domestic pressure, with mass protests planned over his handling of the hostage crisis and his decision to fire the head of Israel's internal security agency. His latest testimony in a long-running corruption trial was cancelled after the strikes.
The main group representing families of the captives accused the government of backing out of the ceasefire, saying it chose to give up on the hostages.
We are shocked, angry and terrified by the deliberate dismantling of the process to return our loved ones from the terrible captivity of Hamas, the Hostages and Missing Families Forum said in a statement.
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