The Israeli military said it has hit targets across Gaza with Hamas-run Health Ministry officials reporting at least 400 people have been killed.
Strikes were reported in multiple locations early on Tuesday, local time, including northern Gaza, Gaza City and Deir al-Balah, Khan Younis and Rafah in central and southern Gaza Strip.
Israel's Lieutenant Colonel Avichay Adraee issued an evacuation notice for the neighbourhoods of Beit Hanoun, Khirbet Khuza'a, Abasan al-Kabira and al-Jadida.
"The IDF has launched a massive offensive against terrorist organizations. These designated areas are considered dangerous combat zones!" his statement on X read.
Palestinian Health Ministry officials said many of the dead were children.
The Israeli military said it had hit dozens of targets in strikes that had targeted mid-level Hamas commanders and leadership officials, as well as infrastructure belonging to the militant group.
It said the attacks would continue for as long as necessary, and would extend beyond air strikes.
Israel's defence minister vowed to press ahead until all remaining hostages are released.
The surprise attack shattered a period of relative calm during the Muslim holy month of Ramadan.
A senior Hamas official said Israeli Prime Minister Benjamin Netanyahu's decision to launch widespread strikes on Gaza amounts to a "death sentence" for the remaining hostages held there.
Izzat al-Risheq, a member of Hamas' political bureau, accused Mr Netanyahu of resuming the war to try and save his far-right governing coalition.
"Netanyahu's decision to return to war is a decision to sacrifice the (Israeli) occupation's captives and a death sentence against them," he said.
The strikes were far wider in scale than the regular series of drone attacks the Israeli military has said it has conducted against individuals or small groups of suspected militants.
They came after weeks of failed efforts to agree an extension to the ceasefire truce, which had been agreed on January 19.
Hamas said Israel had overturned the ceasefire agreement, leaving the fate of 59 hostages still held in Gaza uncertain.
Mr Netanyahu's office accused Hamas of "repeated refusal to release our hostages" and rejecting proposals from US President Donald Trump's Mideast envoy Steve Witkoff.
"Israel will, from now on, act against Hamas with increasing military strength," it said in a statement.
In Washington, a White House spokesperson said Israel had consulted the US administration before it carried out the strikes.
The Israeli army did not provide details about the strikes.
Palestinian health authorities and witnesses contacted by Reuters reported damage in numerous areas of Gaza, where hundreds of thousands have been living in makeshift shelters or damaged buildings.
A building in Gaza City, in the northern end of the strip was hit and at least three houses were hit in Deir Al-Balah in central Gaza.
In addition, the strikes hit targets in the southern cities of Khan Younis and Rafah, according to medics and witnesses.
Negotiations continue as fighting resumes
Negotiating teams from Israel and Hamas had been in Doha, with mediators from Egypt and Qatar trying to secure terms for further phases of the stalled ceasefire deal.
On the weekend, Mr Witkoff, who has been leading mediation efforts along with Egypt and Qatar, warned that Hamas must release living hostages immediately "or pay a severe price".
Under the initial phase in the ceasefire, 33 Israeli and five Thai hostages were returned by militant groups in Gaza in exchange for the release of about 2,000 Palestinian prisoners.
With the backing of the US, Israel had been pressing for the return of the remaining 59 hostages in Gaza in exchange for a longer-term truce.
It would have halted fighting until after the Muslim fasting month of Ramadan and the Jewish Passover holiday in April.
However, Hamas had been insisting on moving to negotiations for a permanent end to the war and a full withdrawal of Israeli forces from Gaza, in accordance with the terms of the original ceasefire agreement.
Each side has accused the other of failing to respect the terms of the January ceasefire agreement, and there were multiple hiccups during the course of the first phase.
But until now, a full return to the fighting had been avoided.
Israel had blocked deliveries of aid from entering Gaza, and had threatened on numerous occasions to resume fighting if Hamas did not agree to return all the hostages.
Much of Gaza is in ruins after 15 months of fighting, which erupted on October 7, 2023 when thousands of Hamas-led terrorists attacked Israeli communities around the Gaza Strip, killing about 1,200 people, according to Israeli tallies, and abducting 251 hostages into Gaza.
The Israeli campaign in response has killed more than 48,000 people, according to Palestinian health authorities, and destroyed much of the housing and infrastructure in the enclave, including the hospital system.
ABC/Wires