The U.N. Security Council is planning an emergency meeting about Iran on Friday, after the USA asked the world body to show support for Iran's anti-government protesters.
In a formal statement from the former S.C. governor, Haley compared protesting Iranians to others living under "oppressive governments" in Cuba, North Korea and Venezuela.
At least 21 people have died and hundreds have been arrested as protests over economic woes turned against the government in Tehran, with attacks on government buildings and police stations.
Iran's prosecutor general, Mohammad Jafar Montazeri, said Thursday that an American CIA official was the "main designer" of the demonstrations.
"Iran's domestic affairs have nothing to do with the United Nations Security Council's role".
U.S. Ambassador Nikki Haley has praised the demonstrators, saying "the United Nations must speak out" on their behalf.
The president's tweets haven't called for violence or disruptive acts, but he has commended the protests, expressing "such respect for the people of Iran as they try to take back their corrupt government" and pledging "great support from the United States".
Presidential Spokesperson İbrahim Kalın said such actions could provoke a backlash, after six days of anti-government protests in Iran. "All freedom-loving people must stand with their cause", she said on Tuesday. But Russia has warned against "external interference" in what it sees as an Iran's internal affairs.
"The whole territory of the U.S.is within the range of our nuclear strike and a nuclear button is always on the desk of my office and this is just a reality, not a threat", he said, while emphasising that the weapons would only be used if North Korea was threatened.
"The U.S. delegation undoubtedly has something to share with the world".
The U.S. State Department did not respond to a requests for comment on Kim's address, but analysts said it was an attempt to weaken the U.S. Iran isn't a member.
The 2015 Iran deal gave Iran sanctions relief in exchange for curbs on its nuclear programme. Trump said Tehran was getting disproportionate benefits, considering its concessions.
The United States imposed sanctions on five Iranian companies it alleges are working on part of the Islamic republic's illegal ballistic missile programme. Earlier in the year, the United Nations its peacekeeping role in Darfur, which caused concern among some human rights activists.