The North Korean ambassador walked out before Mr Donald Trump began speaking, while Iran's Foreign Minister Javad Zarif said "Trump's ignorant hate speech belongs in mediaeval times".
In a bellicose speech at the United Nations General Assembly on Tuesday, President Trump signalled a potential walkout by the US from the 2015 nuclear deal with Iran - which Teheran is in compliance with - and threatened to "totally destroy" North Korea.
It drew praise from Republicans but worried many analysts.
Republican House Speaker Paul Ryan tweeted: "Great message… at the UN. American leadership is needed now more than ever. We must stand by our allies and confront our enemies."
The Democrats thought otherwise. Senator Dianne Feinstein said: "Trump's bombastic threat to destroy North Korea and his refusal to present any positive pathways forward on the many global challenges we face are severe disappointments."
Some say Mr Trump's first address to the General Assembly was actually a domestic speech.
His opening remarks touted economic growth in the US, and a US$700 billion (S$940 billion) boost for the military.
Mr Trump used the UN stage for political theatre, said Professor H.W. Brands, a historian at the University of Texas at Austin.
"This is a clear case of the President focusing more on his domestic audience than foreign audiences. He used inflammatory language to portray himself as tough, which plays well with those who voted for him," he said.
Professor Glenn Altschuler, an expert in American studies at Cornell University, said Mr Trump was "signalling a move towards a more unilateral, narrowly self-interested foreign policy".
Some reactions to Mr Trump's speech on Tuesday.
POWERFUL, CRYSTAL CLEAR
Powerful speech… America's foreign policy was made crystal clear to friend and foe alike.
REPUBLICAN SENATOR ROGER WICKER
TACTICS OF INTIMIDATION
He aims to unify the world through tactics of intimidation, but in reality he only further isolates the United States.
DEMOCRATIC SENATOR DIANNE FEINSTEIN
FIRM AND SPECIFIC
We view the speech as portraying a firm and specific stance on the key issues regarding keeping peace and safety that the international community and the United Nations are faced with.
THE OFFICE OF SOUTH KOREAN PRESIDENT MOON JAE IN
"The 'America First' theme, the military response to North Korea, the likely cancellation of the nuclear deal with Iran, will certainly play well with his base, but are not likely to play well with an international audience," he said.
Some analysts expressed concern. Dr Mira Rapp-Hooper of the Centre for a New American Security said the threat to "totally destroy" North Korea was an "unholy choice between a real threat of deliberate war and a reckless gamble that risks horrid miscalculation".
Mr Daryl G. Kimball, executive director of the Arms Control Association, said: "It is naive to think that sanctions pressure and bellicose US threats of nuclear attack can force North Korea to change course."
Analysts also warned of the risks of upsetting the 2015 deal with Iran,which aims to get the country to divert its nuclear research and production to peaceful use.
An Asian security analyst, who asked not to be named, said Mr Trump's claims that Iran exports terrorism and instability and is violating the "spirit" of the agreement reflects his alignment with Saudi Arabia and Israel.
Israeli Prime Minister Benjamin Netanyahu said he has "never heard a bolder or more courageous speech" at the UN.
The Asian analyst noted the Iran deal was signed by Britain, Russia, France, China and the European Union. Attempts to cancel or renegotiate it will create rifts between the US and Europe, embolden Saudi Arabia, further destabilise the Middle East, draw Russia and China in to back Iran, and create complications for the US in Afghanistan, he said.
"Iran is not a pushover; it is a big country with a strong sense of civilisation and patriotism, with support in Europe and elsewhere," he warned.
Mr Kimball noted that Iran is meeting its commitments. "Further steps by the Trump administration to undermine the Iran nuclear deal will isolate the US… and worst of all, potentially lead to the undoing of the agreement, thereby increasing the threat of war and a spiral of nuclear proliferation in the Middle East and beyond," he said.
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