Ammon News - Israel's military said six waves of missiles were launched by Iran ahead of Trump saying the ceasefire had come into effect.
Israel's ambulance said four people were killed in Beersheba.
Iran's semi-official SNN news agency reported on Tuesday that Tehran fired its last round of missiles before the ceasefire.
Huge explosions were heard in Haifa early Tuesday morning after new Iranian missiles were fired toward Israel.
Trump said in a post on Truth Social that a ceasefire between Israel and Iran was now in place.
His announcement came only hours after Iran launched waves of missiles, which Israel's ambulance service said killed four people.
When Trump announced on Monday what he called a complete ceasefire to end a 12-day war, he appeared to suggest that Israel and Iran would have time to complete missions that were underway, at which point the ceasefire would begin in a staged process.