United Nations (CNN) President Donald Trump delivered Tuesday a doomsday warning to North Korea and mocked its young leader, a pugnacious escalation in rhetoric in a wide-ranging debut address to the United Nations, the world's foremost diplomatic body.

In blunt terms, Trump warned the US would "totally destroy North Korea" if forced to defend itself or its allies. He said while the US has "great strength and patience," its options could soon run out.

Directly putting the country's leader on notice, Trump suggested Kim Jong Un could not survive an American attack.

"Rocket Man is on a suicide mission for himself," he said.

It was a characteristically bombastic approach to a crisis that's growing in scale. Throughout his address -- the most closely watched foreign policy remarks of his presidency -- Trump brought frank assessments to a range of sticky global flashpoints.

He declared the Iran nuclear deal all but dead, saying it was an "embarrassment" to the United States. He bluntly described some regions of the world as "going to hell." And he revived his use of the term "radical Islamic terrorism," vowing to stamp out terrorists worldwide.

But it was Trump's remarks about North Korea that prompted the loudest buzz in the soaring, green-hued General Assembly hall, where Trump spoke to more than 100 world leaders and diplomats.

"It is an outrage that some nations would not only trade with such a nation but would arm, supply and financially support a country that imperils the world," he said.

He warned nations against becoming "bystanders to history" and thanked members of the UN Security Council -- where he's secured key victories through passage of sanctions measures against North Korea -- for escalating their rebukes of Pyongyang.

Iran

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He directed similar ire toward Iran, which he accused of supporting terrorists and destabilizing the region.

"The Iranian government masks a corrupt dictatorship behind the false guise of a democracy," Trump said. "It has turned a wealthy country with a rich history and culture into an economically depleted rogue state whose chief exports are violence, bloodshed and chaos."

He left little doubt to his plans for the nuclear deal, which was brokered under the Obama administration and lifted some sanctions on the country in exchange for curbing aspects of its nuclear program.

"The Iran deal was one of the worst and most one-sided transactions," Trump said. "That deal is embarrassment to the US and I don't think you've heard the last of it, believe me."

Trump faces a mid-October deadline for re-certifying Iran's compliance with the agreement. US officials say Trump is still weighing his next moves and plans to announce his intentions next month.

He also lambasted Venezuela's leader Nicolas Maduro, accusing him of depriving his people in the same of socialist ideas. "The Venezuelan people are starving and their country is collapsing," Trump said.

'Sovereignty'

Photos: President Trump's first foreign trip President Donald Trump and first lady Melania Trump board Air Force One on Saturday, May, 27, 2017, at Naval Air Station Sigonella in Italy. They were headed back to the United States after a nine-day trip to the Middle East and Europe. Hide Caption 1 of 69 Photos: President Trump's first foreign trip President Trump greets people on May 27, after speaking to US troops at Naval Air Station Sigonella. Hide Caption 2 of 69 Photos: President Trump's first foreign trip President Trump addresses US troops and their families on May 27, at the Sigonella Naval Air Station. Hide Caption 3 of 69 Photos: President Trump's first foreign trip President Trump and first lady Melania Trump arrive on May 27, to address US military personnel and families at Naval Air Station Sigonella. Hide Caption 4 of 69 Photos: President Trump's first foreign trip Leaders of the G-7 and some African nations pose for a photo on May 27, on the second day of the G-7 summit in Taormina, Italy. Hide Caption 5 of 69 Photos: President Trump's first foreign trip President Trump gestures on May 27, during a G-7 session. Hide Caption 6 of 69 Photos: President Trump's first foreign trip President Donald Trump and his wife, Melania, arrive for a concert of the La Scala Philharmonic Orchestra while in Taormina, Italy, on Friday, May 26. The Trumps are in Italy for a two-day G-7 summit. Hide Caption 7 of 69 Photos: President Trump's first foreign trip Trump and other leaders pose for a group photo at the G-7 summit on May 26. From left are European Council President Donald Tusk, Canadian Prime Minister Justin Trudeau, German Chancellor Angela Merkel, Trump, Italian Prime Minister Paolo Gentiloni, French President Emmanuel Macron, Japanese Prime Minister Shinzo Abe, British Prime Minister Theresa May and European Commission President Jean-Claude Juncker. Hide Caption 8 of 69 Photos: President Trump's first foreign trip Trump and Trudeau walk together after the group photo. Hide Caption 9 of 69 Photos: President Trump's first foreign trip G-7 leaders congregate during a walking tour on May 26. Hide Caption 10 of 69 Photos: President Trump's first foreign trip Trump embraces new French President Emmanuel Macron on May 26. Hide Caption 11 of 69 Photos: President Trump's first foreign trip The leaders watch a French air squadron. Hide Caption 12 of 69 Photos: President Trump's first foreign trip Melania Trump arrives at the City Hall in Catania, Italy, on May 26. She was wearing a $51,500 Dolce & Gabbana jacket as she met with other spouses of G-7 leaders. Hide Caption 13 of 69 Photos: President Trump's first foreign trip Trump shakes hands with Macron in Brussels, Belgium, on Thursday, May 25. They were attending a NATO summit as the alliance officially opened a new $1 billion headquarters. Hide Caption 14 of 69 Photos: President Trump's first foreign trip Trump stands with other world leaders during a NATO photo shoot on May 25. Hide Caption 15 of 69 Photos: President Trump's first foreign trip Trump speaks with British Prime Minister Theresa May during a working dinner at NATO headquarters. Hide Caption 16 of 69 Photos: President Trump's first foreign trip Trump stands next to German Chancellor Angela Merkel at the NATO summit. Hide Caption 17 of 69 Photos: President Trump's first foreign trip Melania Trump visits the Magritte Museum in Brussels with Amelie Derbaudrenghien, partner of Belgian Prime Minister Charles Michel. Hide Caption 18 of 69 Photos: President Trump's first foreign trip A girl takes a selfie with Melania Trump at a children's hospital in Brussels on May 25. Hide Caption 19 of 69 Photos: President Trump's first foreign trip Trump meets with Macron in Brussels. Hide Caption 20 of 69 Photos: President Trump's first foreign trip Trump walks with European Council President Donald Tusk, center, and European Commission President Jean-Claude Juncker, right, after they met at the European Council in Brussels on May 25. Hide Caption 21 of 69 Photos: President Trump's first foreign trip Trump, third from right, attends a meeting with leaders at the European Council. Hide Caption 22 of 69 Photos: President Trump's first foreign trip Trump speaks with King Philippe of Belgium as Queen Mathilde and Melania Trump chat during a reception at the Royal Palace in Brussels on Wednesday, May 24. Hide Caption 23 of 69 Photos: President Trump's first foreign trip Tusk talks to Trump as he welcomes him in Brussels. Hide Caption 24 of 69 Photos: President Trump's first foreign trip Trump stands with Belgian Prime Minister Charles Michel while the national anthem is played during Trump's arrival in Belgium on May 24. Hide Caption 25 of 69 Photos: President Trump's first foreign trip Protesters in Brussels demonstrate with effigies of Trump and Michel on May 24. Hide Caption 26 of 69 Photos: President Trump's first foreign trip Trump shakes hands with Italian President Sergio Mattarella in Rome on May 24. Hide Caption 27 of 69 Photos: President Trump's first foreign trip Pope Francis stands with Trump and his family during a private audience at the Vatican on May 24. Joining the President, from left, are Trump's son-in-law, White House senior adviser Jared Kushner; Trump's daughter and adviser Ivanka Trump; and first lady Melania Trump. Hide Caption 28 of 69 Photos: President Trump's first foreign trip Trump and the Pope exchange gifts. Trump presented the Pope with a first-edition set of Martin Luther King's writings. The Pope gave Trump an olive-tree medal that the Pope said symbolizes peace. Hide Caption 29 of 69 Photos: President Trump's first foreign trip Trump and his wife look at the ceilings of the Sistine Chapel. Hide Caption 30 of 69 Photos: President Trump's first foreign trip Trump speaks to reporters in Rome during a meeting with Italian Prime Minister Paolo Gentiloni, right, on May 24. Hide Caption 31 of 69 Photos: President Trump's first foreign trip The first lady visits a pediatric hospital in Vatican City on May 24. Hide Caption 32 of 69 Photos: President Trump's first foreign trip Melania Trump arrives at the Vatican on May 24. With Vatican protocol in mind, she wore a black veil and long-sleeved black dress draped down to her calf. Ivanka Trump wore a similar outfit with a larger veil. Hide Caption 33 of 69 Photos: President Trump's first foreign trip President Trump and Israeli Prime Minister Benjamin Netanyahu wave at the Israel Museum in Jerusalem on Tuesday, May 23. Trump gave a speech there, reaffirming his country's commitment to Israel while also holding up Judaism's historical ties to the United States. Hide Caption 34 of 69 Photos: President Trump's first foreign trip People take pictures of the message Trump wrote at Yad Vashem, the Holocaust memorial in Jerusalem, on May 23. Hide Caption 35 of 69 Photos: President Trump's first foreign trip With the help of US Marines, Trump and his wife lay a wreath at Yad Vashem. Hide Caption 36 of 69 Photos: President Trump's first foreign trip Trump meets with Mahmoud Abbas, the President of the Palestinian Authority, on May 23. Trump met with Israeli leaders the day before and said he believes both sides "are ready to reach for peace." Hide Caption 37 of 69 Photos: President Trump's first foreign trip A Palestinian security official takes position before the arrival of Trump's convoy in Bethlehem, West Bank. Hide Caption 38 of 69 Photos: President Trump's first foreign trip Israeli and American activists hold signs Monday, May 22, during an anti-Trump protest next to the US embassy in Tel Aviv, Israel. Hide Caption 39 of 69 Photos: President Trump's first foreign trip Melania Trump and Israeli first lady Sara Netanyahu speak to children during their visit to the Hadassah hospital in Jerusalem on May 22. Hide Caption 40 of 69 Photos: President Trump's first foreign trip Trump talks to reporters as he meets with Israeli Prime Minister Benjamin Netanyahu on May 22. Trump sought to rebut claims that he damaged Israeli intelligence capabilities by revealing highly classified information to Russian operatives earlier this month. "Just so you understand, I never mentioned the word or the name Israel," Trump told reporters as he began the second leg of his first foreign tour. Hide Caption 41 of 69 Photos: President Trump's first foreign trip Trump touches the Western Wall, Judaism's holiest prayer site, while in Jerusalem on May 22. Trump became the first sitting US president to visit the wall. Hide Caption 42 of 69 Photos: President Trump's first foreign trip Trump stands in the Western Wall plaza. To his left, in black, is Shmuel Rabinowitz, the rabbi of the Western Wall. Hide Caption 43 of 69 Photos: President Trump's first foreign trip First lady Melania Trump, in white, visits the Western Wall. At far left is Ivanka Trump. Hide Caption 44 of 69 Photos: President Trump's first foreign trip The President and first lady plant a tree in Jerusalem with Israeli President Reuven Rivlin. Hide Caption 45 of 69 Photos: President Trump's first foreign trip Trump is welcomed by Netanyahu upon arriving in Tel Aviv on May 22. Trump started his trip with two days in Saudi Arabia. Hide Caption 46 of 69 Photos: President Trump's first foreign trip On the way to Tel Aviv, US Secretary of State Rex Tillerson speaks with reporters aboard Air Force One. Hide Caption 47 of 69 Photos: President Trump's first foreign trip While in Riyadh, Saudi Arabia, Trump attends the inauguration ceremony for the Global Center for Combating Extremist Ideology. Joining him here are Saudi King Salman bin Abdulaziz Al Saud, center, and Egyptian President Abdel Fattah el-Sisi, left. Hide Caption 48 of 69 Photos: President Trump's first foreign trip Trump speaks in Riyadh during the Arab Islamic American Summit on Sunday, May 21. Trump looked to make it clear that the United States is not at war with Islam. "This is not a battle between different faiths, different sects or different civilizations," he said. "This is a battle between barbaric criminals who seek to obliterate human life, and decent people of all religions who seek to protect it. This is a battle between good and evil." Hide Caption 49 of 69 Photos: President Trump's first foreign trip Trump sits at the summit, which included leaders from 55 Muslim-majority countries. He urged them to do more to eradicate terrorist groups that claim the mantle of Islam. "We can only overcome this evil if the forces of good are united and strong and if everyone in this room does their fair share and fulfills their part of the burden," Trump said. "Muslim-majority countries must take the lead in stamping out radicalization." Hide Caption 50 of 69 Photos: President Trump's first foreign trip Trump poses with other leaders at the Arab Islamic American Summit. Hide Caption 51 of 69 Photos: President Trump's first foreign trip Saudi King Salman shakes hands with Trump on May 21. Trump is the first US president to start his first foreign trip in the Middle East. Hide Caption 52 of 69 Photos: President Trump's first foreign trip Trump meets with other heads of state in Riyadh on May 21. Hide Caption 53 of 69 Photos: President Trump's first foreign trip Trump speaks with the Crown Prince of Abu Dhabi, Gen. Sheikh Mohammed Bin Zayed Al Nahyan. Hide Caption 54 of 69 Photos: President Trump's first foreign trip First lady Melania Trump chats with children during a visit to the American International School in Riyadh on May 21. Hide Caption 55 of 69 Photos: President Trump's first foreign trip While in Riyadh, President Trump meets with Bahrain's King Hamad bin Isa Al Khalifa on May 21. Hide Caption 56 of 69 Photos: President Trump's first foreign trip President Trump and Egyptian President Abdel Fattah el-Sisi share a laugh during a meeting on May 21. El-Sisi complimented Trump on his "unique personality that is capable of doing the impossible." Trump exchanged pleasantries back, praising el-Sisi's shoes. Hide Caption 57 of 69 Photos: President Trump's first foreign trip Trump is handed a sword during a welcoming ceremony at Riyadh's Murabba Palace on Saturday, May 20. Hide Caption 58 of 69 Photos: President Trump's first foreign trip Trump sits with members of his staff and Cabinet before a meeting with Saudi King Salman on May 20. Hide Caption 59 of 69 Photos: President Trump's first foreign trip Trump and King Salman take part in a signing ceremony at the Saudi Royal Court in Riyadh on May 20. The two leaders oversaw the signing of a defense deal worth nearly $110 billion. Hide Caption 60 of 69 Photos: President Trump's first foreign trip The Trumps look at a display of modern art at the Saudi Royal Court in Riyadh. Hide Caption 61 of 69 Photos: President Trump's first foreign trip King Salman presents Trump with a gilded necklace and medal, the country's highest honor. The distinction also was bestowed upon Presidents Barack Obama and George W. Bush. Hide Caption 62 of 69 Photos: President Trump's first foreign trip The first lady chats with Saudi Crown Prince Muhammad bin Nayef at the medal ceremony on May 20. Hide Caption 63 of 69 Photos: President Trump's first foreign trip Ivanka Trump attends the medal ceremony. Hide Caption 64 of 69 Photos: President Trump's first foreign trip Trump meets with King Salman after arriving in Riyadh on May 20. Hide Caption 65 of 69 Photos: President Trump's first foreign trip Soldiers on horseback carry the US and Saudi flags as they escort Trump to the Saudi Royal Court in Riyadh. Hide Caption 66 of 69 Photos: President Trump's first foreign trip Trump is welcomed by King Salman after arriving at the King Khalid International Airport in Riyadh. Hide Caption 67 of 69 Photos: President Trump's first foreign trip The Trumps take part in the welcome ceremony. Hide Caption 68 of 69 Photos: President Trump's first foreign trip The President and first lady wave from Air Force One after landing in Riyadh. Hide Caption 69 of 69

Trump has delivered major foreign policy addresses before, but the issues at the United Nations are broader and the geographic spread of Trump's audience wider. The message he delivered here will resonate in capitals worldwide, where officials and leaders are still seeking a cohesive foreign policy doctrine from new American leader.

In his remarks, Trump sought to encapsulate his worldview through the theme of "sovereignty," suggesting that nations acting in their own self-interest would create a more stable world.

"As President of the United States, I will always put America first, just like you, as the leaders of your countries, will always and should always put your countries first," he said to scattered applause. "All responsible leaders have an obligation to serve their own citizens, and the nation-state remains the best vehicle for elevating the human condition."

Trump told world leaders that he would not insist their countries adopt US values.

"In America, we do not seek to impose our way of life on anyone, but rather to let it shine as an example for everyone to watch," Trump said.

For a President whose election and elevation to the White House was among the most improbable in modern political history, the United Nations stage represented a milestone, even if some in the audience still find the sight of Trump in front of the iconic green marble jarring . Trump's three eldest children -- Donald Jr, Ivanka and Eric Trump -- all attended his speech, along with first lady Melania Trump.

Trump's remarks, which ran 41 minutes long, were written with the help of Stephen Miller, Trump's senior policy adviser who also acts as the presidential speechwriter. Miller's nationalist worldview was evident throughout, from Trump's critiques of free trade agreements to his insistence that refugees are better resettled in their own regions than in the United States. In a return to a campaign-style phrase, Trump declared that America's middle-class would be "forgotten no more."

So, too, was Miller's voice evident in Trump's use of the phrase "radical Islamic terror," a loaded term that some argue unfairly impugns an entire religion. Trump, who employed the term frequently on the campaign trail, curtailed its use as President. But he returned to the description on Tuesday, claiming his administration had done more to go after groups like ISIS than his predecessor.

"Our military will soon be the strongest it's ever been," he said.

UN criticism

Trump has demeaned the United Nations in the past, claiming the body is ridden with bureaucracy and overspending. His first remarks as president here on Monday were centered on reforming the institution's practices.

During his address, however, Trump was optimistic about the UN's ability to improve global security through collective action.

"Major portions of the world are in conflict, and some in fact are going to hell, but the powerful people in this room, under the guidance and auspices of the United Nations, can solve many of these vicious and complex problems," he said.

In his remarks, Trump made no mention of climate change, an issue the United Nations has worked to combat through the Paris accord, an agreement Trump has lambasted. He also made few references to Russia, whose actions in Ukraine have caused deep anxiety throughout Europe.

Among the hundreds of diplomats assembled to watch his speech, reaction was largely muted. He received applause for declaring that countries should act in their own interest and for his backing of women's equality, but only bemused murmurs for his bellicose threats toward North Korea.