The directive by Israel Katz on Tuesday followed an announcement by the military that it had detected missile launches from Iran towards Israel.
Less than three hours earlier, US President Donald Trump had said the ceasefire was in effect.
Katz said the military had now been instructed to carry out high-intensity operations against targets in Tehran.
Earlier, Israeli Prime Minister Benjamin Netanyahu said Israel had agreed to Trump's ceasefire proposal, declaring Israel had achieved its goal of removing Iran's nuclear and ballistic missile threat, but warned it would respond forcefully to any violations, his office said.
Writing on Truth Social earlier, Trump declared: "THE CEASEFIRE IS NOW IN EFFECT. PLEASE DO NOT VIOLATE IT!"
His announcement on Tuesday came after Iran launched a fresh wave of missiles, killing four people, according to paramedics, and as Iranian authorities reported nine people killed in an attack in northern Iran on Tuesday morning.
When Trump announced on Monday what he called a complete ceasefire to end the war, he appeared to suggest Israel and Iran would have time to complete missions that were under way, at which point the ceasefire would begin in a staged process.
His declaration came after a sharp escalation of the conflict since Sunday, when the United States bombed Iranian nuclear sites, prompting Iran to retaliate by firing missiles at a US base in Qatar on Monday.
Early on Tuesday, witnesses said they heard explosions near Tel Aviv and Beersheba in southern Israel, while Iran's semi-official SNN news agency reported Tehran fired its last round of missiles before the ceasefire came into effect.
Israel's military said six waves of missiles were launched by Iran and Israel's national ambulance service said four people were killed in Beersheba.
In Iran, the deputy governor of the northern province of Gilan said four residential units were destroyed in a "terrorist attack" on Tuesday morning, killing nine people and injuring 33.
A senior White House official said Trump had brokered the ceasefire deal in a call with Netanyahu and Israel had agreed so long as Iran did not launch further attacks.
An Iranian official earlier confirmed Tehran had agreed to a ceasefire, but the country's foreign minister said there would be no cessation of hostilities unless Israel stopped its attacks.
Abbas Araqchi said if Israel stopped its "illegal aggression" against the Iranian people no later than 4am Tehran time (10.30am AEST) on Tuesday, Iran had no intention of continuing its response.
Israel, joined by the United States at the weekend, carried out attacks on Iran's nuclear facilities after alleging Tehran was getting close to obtaining a nuclear weapon.
Iran denies ever having a nuclear weapons program but Supreme Leader Ali Khamenei has said that if it wanted to, world leaders "wouldn't be able to stop us".
Qatari Prime Minister Sheikh Mohammed bin Abdulrahman Al Thani secured Tehran's agreement during a call with Iranian officials, an official briefed on the negotiations said.
US Vice-President JD Vance, Secretary of State Marco Rubio and US special envoy Steve Witkoff were in direct and indirect contact with the Iranians, a White House official said.
Hours earlier, three Israeli officials had signalled Israel was looking to wrap up its campaign in Iran and had informed the United States.
Earlier on Monday, Trump said he would encourage Israel to proceed towards peace after dismissing Iran's attack on an American air base that caused no injuries and thanking Tehran for early notice of the strikes.
He said Iran fired 14 missiles, calling it "a very weak response, which we expected, and have very effectively countered".
Iran's attack came after US bombers dropped 13.6-tonne bunker-buster bombs on Iranian underground nuclear facilities at the weekend, joining Israel's air war.
The Trump administration maintains its aim was solely to destroy Iran's nuclear program, not to open a wider war.
Trump has cited intelligence reports that Iran was close to building a nuclear weapon, without elaborating.
However, US intelligence agencies said earlier in 2025 they assessed that Iran was not building a nuclear weapon.
with AP
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