"Hamas is not the Hamas of two years ago. Hamas has been defeated every place we fought them," Brigadier General Effie Defrin told reporters at a briefing.
He urged Palestinian residents of the Gaza Strip to avoid entering areas under control by the Israel Defence Forces in the enclave.
"I am calling from here on the residents of Gaza to avoid entering areas under IDF control. Keep to the agreement and ensure your safety," he said.
Thousands of displaced Palestinians began flocking towards their abandoned homes after a US-brokered ceasefire took effect on Friday and Israeli troops began pulling back from parts of the strip.
A huge column of displaced Gazans filed north through the dust and rubble towards Gaza City, the enclave's biggest urban area, which had been under attack just days ago in one of Israel's biggest offensives of the war.
"Thank God my house is still standing," said Ismail Zayda, 40, in the Sheikh Radwan district of Gaza City.
"But the place is destroyed, my neighbours' houses are destroyed, entire districts have gone."
The Israeli military said the ceasefire agreement had been activated at noon local time.
Israel's government ratified the ceasefire with Hamas in the early hours of Friday, clearing the way to partially pull back troops and fully suspend hostilities in the enclave within 24 hours.
Hamas is expected to release the 20 living Israeli hostages within 72 hours, after which Israel will release 250 Palestinians serving long terms in Israeli prisons and 1700 others detained in the Gaza Strip during the war.
US Special Envoy to the Middle East Steve Witkoff said the Israeli military had completed the first phase of a withdrawal and the hostage release period had started.
Once the agreement is operating, trucks carrying food and medical aid will surge into the Gaza Strip to help civilians, hundreds of thousands of whom have been sheltering in tents after Israeli forces destroyed their homes and razed entire cities.
The first phase of US President Donald Trump's initiative to end the two-year war calls for Israeli forces to withdraw from some of the Gaza Strip's major urban areas although they will still control roughly half of the enclave's territory.
In a televised address, Prime Minister Benjamin Netanyahu said Israeli forces would stay in the strip to ensure the territory was demilitarised and Hamas disarmed in future stages of the plan: "If this is achieved the easy way then that will be good, and if not then it will be achieved the hard way."
