"The matter can be deemed concluded," Iran's mission to the United Nations said in a post on X just a few hours after the start of the operation late Saturday.
"However, should the Israeli regime make another mistake, Iran's response will be considerably more severe," the Iranian mission warned.
No Iranian leaders have spoken out to justify the attack, which marked the first time Iran has launched a direct military assault on Israeli territory.
Late Saturday, Iran's Revolutionary Guards Corps announced that they had launched "dozens of drones and missiles" towards military sites on Israeli territory.
"Iran's military action was in response to the Zionist regime's aggression against our diplomatic premises in Damascus," the Iranian mission to the UN said.
The attack, according to the mission, was "conducted on the strength of Article 51 of the UN Charter pertaining to legitimate defense".
However Israel's army said it had shot 99 percent of the drones and missiles with the help of the United States and other allies, declaring Iran's attack "foiled".
Experts have suggested that Saturday's slow-moving drone attack was calibrated to represent a show of power but also allow some wiggle room.
"It appears that Iran telegraphed its attack on Israel to demonstrate it can strike using different capabilities to complicate the (Israeli army's) ability to neutralise the assault but also to provide an off ramp to pause escalation," said Nishank Motwani, senior analyst at the Australian Strategic Policy Institute in Washington.
- Attack 'telegraphed' -
Over the last two weeks, the Iranian authorities repeatedly vowed to "punish" Israel after the death of seven Guards including two generals of the Quds Force in an attack that levelled the Iranian consulate in Damascus on April 1.
Iran has blamed Israel for the attack.
In the days after the strike, Iran's Supreme leader Ayatollah Ali Khamenei said Israel will be "slapped for that action".
Since a revolution in 1979 in Iran which toppled the US-backed Shah, Israel has been the sworn enemy of the Islamic Republic.
Iran has often called for the destruction of Israel, with support of the Palestinian cause one of the pillars of the Islamic revolution.
However Tehran had also refrained from a direct attack on Israel -- until Saturday.
Instead, it has backed members of the so-called "Axis of Resistance" against Israel, including Lebanon-based militant group Hezbollah and Yemen's Huthi rebels, since the outbreak of war in Gaza between Israel and Palestinian militant group Hamas on October 7.
Hours before the strikes on Saturday, Iran seized an Israeli-linked container ship in the Gulf which Washington called "an act of piracy".
- 'Next slap will be fiercer' -
During the night, Tehran also warned the United States, urging them to "stay away" from its conflict with Israel.
"Any threat by the terrorist government of America and the Zionist regime from any country will result in a reciprocal and proportionate response," the Revolutionary Guards warned in a statement early Sunday.
"If necessary", Tehran "will not hesitate to take defensive measures to protect its interests against any aggressive military action," Iran's Ministry of Foreign Affairs said.
"The next slap will be fiercer," warned the new mural unveiled overnight in Tehran's Palestine Square, where a few thousand people gathered during the night shouting "Death to Israel" and "Death to America".
Before Tehran launched its attack, Israel warned Iran that it would suffer "the consequences for choosing to escalate the situation any further".
Israel has not revealed what a potential response would look like.
An Israeli attack on Iran's territory, possibly targeting military or nuclear sites, could not be ruled out, according to experts.
As a precaution, Tehran's Mehrabad airport, which is mainly dedicated to domestic flights, will remain closed on Sunday until 12 pm (0830 GMT), according to the Mehr news agency.
Several international airlines have suspended flights over Iranian airspace.
Countries including Russia and France have also asked their citizens to avoid travelling to Iran and Israel.