According to reports, there have been disagreements over whether to continue on to phase two of the ceasefire, where a permanent peace will be negotiated, or extend phase one.
Israel says it is stopping all goods and supplies into Gaza.
Prime Minister Benjamin Netanyahu’s office claimed Hamas has refused to “accept the Witkoff outline for continuing the talks, which Israel agreed to”.
Under a plan put forward by US Middle East envoy Steve Witkoff, the first phase of the ceasefire deal would continue through Ramadan and Passover, or until 20 April.
Israel said in a statement that Mr Netanyahu “decided that starting this morning, all entry of goods and supplies into the Gaza Strip would cease”.
It added: “Israel will not allow a ceasefire without the release of our hostages.
“If Hamas continues its refusal, there will be further consequences.”
The holy month of Ramadan started on Friday and is usually between 29 and 30 days. Pictures emerged from Gaza of Palestinians celebrating among the rubble.
The Jewish holiday of Passover is shorter, but this year finishes on Sunday 20 April.
The first phase of the previously agreed ceasefire expired on Saturday.
Phase one halted 15 months of fighting and saw the release of 33 Israeli hostages held in Gaza and five Thai nationals, in exchange for around 2,000 Palestinian prisoners and detainees.
The extension would push back phase two of the ceasefire, which was intended to introduce talks to bring about a permanent end to the war.
Hamas said earlier on Saturday the group rejected Israel’s “formulation” of extending the first phase of the ceasefire in Gaza, but did not explicitly mention Mr Witkoff’s plan.
Hamas’s response to the plan is not yet clear.
Both sides have previously traded accusations that the other violated the fragile ceasefire.
Meanwhile, talks on the long-term future of Gaza are yet to seriously materialise after the UN said it would take decades to rebuild the enclave.
Israeli statement
A statement from the prime minister’s office originally published in Hebrew said that on the first day of the proposed extension, half of the hostages and bodies of the dead would be released.
It added that at the end, if an agreement on a permanent ceasefire was reached, the remaining hostages and bodies would also be released.
The statement added: “Witkoff proposed the outline for extending the ceasefire after he was impressed that at this stage there was no possibility of bridging the positions of the parties to end the war, and that additional time was needed for talks on a permanent ceasefire.”
It went on to add that Israel could return to fighting “after the 42nd day if it feels that the negotiations are ineffective”, pointing out that this was supported by the Trump administration.
It isn’t clear what dates these days correspond to.