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The Israel Defense Forces (IDF) said it was targeting what it called "terror targets" belonging to Hamas.
Israeli Prime Minister Benjamin Netanyahu and Defence Minister Israel Katz ordered the strikes on Tuesday morning, according to a statement from the PM's office.
"This follows Hamas's repeated refusal to release our hostages, as well as its rejection of all of the proposals it has received from US Presidential Envoy Steve Witkoff and from the mediators," it said.
"Israel will, from now on, act against Hamas with increasing military strength," it added.
The plan for the strikes "was presented by the IDF over the weekend and approved by the political leadership", it said.
Israel's Ambassador to the UN, Danny Danon, warned Hamas to release all the hostages, stating "we will show no mercy on our enemies".
Hamas has responded furiously, accusing Israel of treachery for overturning the ceasefire agreement. It also says Israel is exposing the remaining Israeli hostages held in Gaza to "an unknown fate".
But Hamas has not yet declared that it is resuming the war, instead calling on mediators and the United Nations to intervene.