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.
Earlier, Iran launched missiles at Israel in the first such bombardment since a fragile ceasefire took effect in early April.
The exchange raised the possibility of a return to heavy fighting and complicating mediation efforts to end the war.
The attack came after US President Donald Trump reportedly told Israeli Prime Minister Benjamin Netanyahu not to strike back after Iran fired a salvo of missiles at Israeli targets in retaliation for an attack on the outskirts of Beirut.
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.
But 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's Revolutionary Guards said they had targeted Ramat David air base, near Nazareth.
The Israeli military said it identified missiles launched from Iran and that its defence systems had intercepted them.
with AP and DPA
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