Although an official said that the Iranian leader's phone would be replaced with a more secure device, he did not reveal further details or suggest who had hacked the phone.
"Confronting multilateralism is not a sign of strength. Rather, it is a symptom of a weakness of intellect," the Iranian president told the U.N. General Assembly.
"Even if Trump himself is interested in negotiations, the people around him are committed to not letting that happen," said the president of the National Iranian American Council.
Secretary of State Mike Pompeo said on Sunday that President Donald Trump is "happy to talk with folks at any time."
Iranian military spokesman Abolfazl Shekarchi has said the attack was carried out by groups linked to the U.S. and Israeli intelligence.
Washington has repeatedly stated it is not interested in a 'regime change' in Tehran.
Despite Khamenei promising that war is not an option, he also said that dialogue with Washington is not on the table.
"I am asking for WORLD PEACE, nothing less!" Trump said in early-morning tweet.
"Even in the worst case, I promise that the basic needs of Iranians will be provided. We have enough sugar, wheat and cooking oil. We have enough foreign currency to inject into the market," Rouhani said.
"If the current capabilities of the Revolutionary Guards ... reaches the ears of the adventure-seeking president of America, he will never make this kind of mistake."
Israeli Prime Minister Benjamin Netanyahu said that "major powers have spoiled Iran" as he joined President Donald Trump in isolating the Islamic Republic.
"Don't play with fire, or you will regret."
President Hassan Rouhani's chief of staff said the current Iranian administration and the Iranian people "will not yield to pressure."
Macron responded to Rouhani by saying that he "hoped that Iran, for its part, will fulfill its obligations without any ambiguity."
Iranian officials have called for users to leave the encrypted messenger and move to a homemade alternative, complete with "death to America" and "Let's pray" stickers.
Iranian Foreign Minister Mohammad Javad Zarif said one option "would involve resuming at a much greater speed our nuclear activities."
Speaking at a military showcase, President Rouhani blamed "invading powers" for shoring up presence around Iran.