Iranian state television reported the sound of explosions being heard in Isfahan, Tabriz and Tehran, without immediately elaborating.
Iran closed the airspace around Tehran's Imam Khomeini International Airport, the country's main airfield, after the Israeli attack.
Israel's Defense Force confirmed the strikes early on Monday on a post on X.
The attacks further strain efforts to reach a permanent ceasefire in the war between Iran and the United States.
US President Donald Trump said on Sunday that new strikes by Israel and Iran would not affect his administration's peace talks with Tehran, saying Israeli Prime Minister Benjamin Netanyahu "doesn't call the shots".
Trump has leaned on Israel to stop its attacks in Lebanon to allow room for a deal to end the wider war with Iran, including rebuking Netanyahu with obscenities in a phone call last week.
However, Israel earlier on Sunday launched strikes in the Beirut area for the first time since the US announced a truce plan for Lebanon last week.
Iran fired a salvo of missiles at Israeli targets in retaliation, putting US-Iran peace talks at risk. But Trump insisted that an agreement to end the wider war remains well within reach.
"It's not going to have any impact on the deal," Trump told the Financial Times.
"I call the shots. I call all the shots. He doesn't call the shots."
Iran has long said any peace deal with the US would depend on a ceasefire also holding in Lebanon, which Israel invaded in March in pursuit of Iran-backed Hezbollah fighters who fired rockets and drones across the border in solidarity with Tehran.
with AP and DPA
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