The letter comes as Israeli Prime Minister Benjamin Netanyahu began a tour of Europe created to turn European leaders' support for a revived accord into a US-style exit from it.
Israeli Prime Minister Benjamin Netanyahu said he was not "surprised" with Iran's move and that Israel will not allow Tehran to get nuclear weapons.
On the agenda will be the nuclear deal with Iran as well as how to push Iranian forces out of Syria.
Major General Ali Jafari, commander of Iran's Revolutionary Guards, said past year that it had missiles with a 2,000-km (1,240-mile) range that could hit arch-enemy Israel and "most American interests and forces" in the Middle East.
It is not yet known whether European countries will keep afloat the deal, which strictly limits Iran's uranium enrichment and is aimed at denying it a nuclear weapons capability.
Prior to embarking on his three-day European tour, Netanyahu made clear that he would press Merkel, Macron, and May to quit the pact. "I am telling the Europeans, limiting our missile work is a dream that will never come true".
Mr Netanyahu is to meet Emmanuel Macron, France's president, in Paris, later today and Theresa May tomorrow. Christophe Petit Tesson/Pool via Reuters.
Israel's Minister of Intelligence Yisrael Katz said Tuesday that a US-led military coalition would confront Iran if it resumed its enrichment of military-grade uranium.
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The other signatories to the accord - Britain, France, Russia, China, and Germany - said they remain committed to the deal.
Western powers view Iran's meddling as destabilizing for the region while Israel sees it as a direct threat to its existence.
The supreme leader also reiterated his support for the country's ballistic missile program.
The remaining backers and parties to the agreement, however, have limited influence on Washington, whose wrath they also face after Mr Trump warned that the U.S. would impose sanctions on companies that continue to do business with Iran. But several large firms have said it will be impossible to continue operating in Iran except in the unlikely scenario that they win bulletproof exemptions from Washington.
That has left Europe under pressure from Tehran.
Iranian Foreign Minister Mohammad Javad Zarif said Sunday the USA decision to withdraw from the agreement was illegal and he urged the other signatories not to follow suit.
The ministers' comments come a day after Ayatollah Khamenei announced that Iran would inform the United Nations nuclear watchdog that preparations for increasing uranium enrichment capacity would begin on Tuesday.
If Israel discovers that Iran has resumed the development of its nuclear program and is advancing it, "a US-led global coalition will threaten and then deal Iran a military blow".