French President Emmanuel Macron spoke with Israeli Prime Minister Benjamin Netanyahu and pressed the importance of maintaining Iran's nuclear accord, the Elysee Palace said on Saturday.
Mr Lavrov, who is Russia's top diplomat, stressed that Russian Federation will work to preserve the existing Iran nuclear deal, and warned that any threat to it also represented a threat to any diplomatic breakthrough with North Korea.
His ultimatum puts pressure on Europeans - key backers and parties to the 2015 worldwide agreement to curb Iran's nuclear programme - to satisfy Trump, who wants the pact strengthened with a separate agreement within 120 days.
Meanwhile, on his official Twitter account, Iran's Foreign Minister Javad Zarif said Trump's decision undermined the multilateral agreement.
Trump's announcement did include new sanctions against 14 Iranian individuals and entities that have committed alleged human rights abuses or supported the country's ballistic missile programs, which are outside the purview of the nuclear deal.
But the strongest reaction came from Tehran, which agreed under the deal to curb its nuclear program and allow intrusive inspections of its nuclear facilities in exchange for relief from punishing economic sanctions.
Trump may eventually sabotage the nuclear deal, but the U.S. will pay a heavy political price.
Trump has repeatedly threatened to tear up what he has described as "the worst deal ever negotiated".
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Iran argues that continued USA sanctions on non-nuclear areas such as human rights and missile testing have effectively barred it from gaining numerous financial benefits expected from the deal.
They are also the first concrete global response to the Iranian government's treatment of protesters.
The Iranian Ministry of Foreign Affairs on Saturday criticised the fresh sanctions imposed by the U.S. by calling them illegal and hostile and warned that they would receive a serious reaction by the Islamic republic.
Trump delivered a blunt ultimatum to European powers, saying, "Fix the deal's disastrous flaws, or the United States will withdraw from the agreement". In effect, he is asking them to act as mediators to accomplish changes that Iran is refusing to make. "No one should doubt my word".
Under increased scrutiny, Tehran on Saturday lifted restrictions on Telegram, acknowledging that the social networking app had been "filtered" during the protests, state media reported.
Iranian officials said Sunday that hundreds of people detained in recent weeks during anti-government protests have been released and acknowledged that at least 25 people were killed during the unrest.