Trump has set a May 12 deadline to "fix" the 2015 accord, which curbs Tehran's nuclear programme in exchange for sanctions relief and was the fruit of intense diplomacy involving the US, European powers, Russia and China.
"There are attempts to interfere with the international order upon which the United Nations depends," Lavrov said after talks with his Chinese counterpart Wang Yi in Beijing.
"We said clearly with China that we will stop attempts to sabotage these agreements that were passed in a UN Security Council resolution," Lavrov said.
He was speaking on the eve of a meeting of the Shanghai Cooperation Organisation, a regional security bloc spearheaded by Moscow and Beijing.
Calling the Iran agreement "one of the biggest achievements in international diplomacy in recent times", Lavrov said that "revising this document is unacceptable".
Trump has threatened to abandon the accord unless European capitals agree to supplement it with tougher controls on Iran's missile programme and its future ability to enrich nuclear fuel.
His partners maintain that implementation of the agreement under the Joint Comprehensive Plan of Action is the best way to prevent Tehran from seeking an atomic bomb.
Iran warned Saturday it was ready to "vigorously" resume nuclear enrichment if the United States ditches the deal.
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