President Masoud Pezeshkian said Iran would "give an appropriate response" to the attack, which killed at least four soldiers, adding that Tehran did not seek war.
Israel said it targeted military sites in several regions of Iran on Saturday in retaliation for Iranian attacks, including a barrage of almost 200 ballistic missiles fired towards Israel on 1 October.
On Sunday Prime Minister Benjamin Netanyahu said Israel had crippled Iranian air defence and missile production systems. He said the strikes had "severely damaged Iran’s defence capability and its ability to produce missiles".
"The attack was precise and powerful and achieved its goals," Netanyahu said at a ceremony commemorating the victims of last year's 7 October attacks.
"This regime must understand a simple principle: whoever hurts us, we hurt him."
Official Iranian sources have publicly played down the impact of the attack, saying most missiles were intercepted and those that weren't caused only limited damage to air defence systems.
In his first public comments since the attack, Khamenei said: "It is up to the authorities to determine how to convey the power and will of the Iranian people to the Israeli regime and to take actions that serve the interests of this nation and country."
President Pezeshkian largely echoed the supreme leader's language, telling a cabinet meeting: "We do not seek war, but we will defend the rights of our nation and country."
The Israeli strikes were more limited than some observers had been expecting. The US had publicly pressured Israel not to hit oil and nuclear facilities, advice seemingly heeded by Tel Aviv.
The Iranian foreign minister said on Sunday that Iran had "received indications" about an impending attack hours before it took place.
"We had received indications since the evening about the possibility of an attack that night," Abbas Araghchi told reporters, without going into more detail.
Western countries have urged Iran in turn not to respond in order to break the cycle of escalation between both Middle Eastern countries, which they fear could lead to all-out regional war.
Iranian media has carried footage of daily life continuing as normal and framing the "limited" damage as a victory, a choice analysts said was intended to reassure Iranians.
Fighting continued between Israel and Iran-backed Hezbollah in Lebanon and between Israel and the Palestinian armed group Hamas in Gaza.
On Sunday, an Israeli air strike on the town of Sidon in southern Lebanon killed at least eight people, according to local authorities. Late on Sunday Lebanon said at least 21 people had been killed in Israeli strikes on the south of the country.
In Gaza, nine people were killed in an Israeli strike on a school-turned-shelter in the al-Shati refugee camp, Palestinians officials said. Palestinian media and the Reuters news agency said three of the dead were Palestinian journalists, citing government officials.
And in Israel, a man was killed and at least 30 injured after a truck hit a bus stop near an Israeli military base north of Tel Aviv, in what authorities said was a suspected terror attack.
Egyptian President Abdel Fattah al-Sisi on Sunday proposed a two-day ceasefire in Gaza, which would involve an exchange of four Israeli hostages for some Palestinian prisoners.
He said that within 10 days of implementing such a temporary ceasefire, talks should resume with the aim of reaching a more permanent one.
But speaking to the BBC's Arabic Service, a senior Hamas official said its conditions for a ceasefire - rejected by Israel for months - have not changed.
Sami Abu Zuhri said the Palestinian militant group continued to demand a complete ceasefire, a full Israeli withdrawal from Gaza and a serious prisoner swap deal.
"Any agreement that does not guarantee these conditions holds no value," he added.
Israel launched a campaign to destroy Hamas in response to the group's unprecedented attack on southern Israel on 7 October 2023, in which about 1,200 people were killed and 251 others were taken hostage.
More than 42,924 people have been killed in Gaza since then, according to the territory's Hamas-run health ministry.
Ido Vock