"The evil regime made a mistake in this regard. It must be punished and will be punished," Khamenei said in a televised speech after Eid al-Adha prayers in Tehran.
Israeli Foreign Minister Israel Katz swiftly riposted with a Persian-language statement on social media site X.
"If Iran attacks from its territory, Israel will respond and attack Iran," he said.
Khamenei said the April 1 strike, which levelled the five-storey Iranian consulate building in the Syrian capital, had run roughshod over international agreements providing for the inviolability of diplomatic premises.
"The consulate and embassy offices in any country are the territory of that country," he said. "When they attacked our consulate, it means they attacked our territory."
Khamenei has led Iranian officials in a succession of promises to avenge the strike, which was widely blamed on arch foe Israel.
One of his senior advisers, Yahya Rahim Safavi, warned on Sunday that Israeli embassies were "no longer safe".
Israel said last week it was strengthening its defences and pausing leave for combat units following Iran's retaliation threats.
Iran does not recognise Israel, and the two countries have fought a shadow war for years.
Iran charges that Israel was behind a wave of sabotage attacks and assassinations targeting its nuclear programme.
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