In his first major address to the United Nations General Assembly on Tuesday, President Trump delivered his harshest warning yet to the North Korean regime, saying it risked "total destruction" if it continues its pursuit of nuclear weapons.

"The U.S. has great strength and patience but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea," said Mr. Trump to the UNGA.

The president also said of North Korean dictator Kim Jong Un, "Rocket Man is on a suicide mission for himself and his regime." It's a nickname he has recently started using in tweets.

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Mr. Trump said the regime's "reckless pursuit of nuclear weapons and ballistic missiles" threatens the entire world with unthinkable loss of human life.

"It is an outrage that some nations would not only trade with such a regime -- but arm, supply and financially support a regime that imperils the world with nuclear conflict."

Describing the North as a "depraved regime," Mr. Trump blamed it for "the starvation deaths of millions, and for imprisonment torture and oppression of countless more," and he cited the case of American student Otto Warmbier, who died after being held in North Korean captivity.

NATO Secretary General Jens Stoltenberg told CBS that Mr. Trump's comments toward North Korea was yet another example of his "strong rhetoric and strong language."

"We've seen the international community condemning North Korea of the developing of nuclear weapons and long-range missiles, the importance of working together to make sure that North Korea bounds it missile program and refrains from more testing, it is a threat toward all of us and it requires a global response," said Stoltenberg.

He added, "there's no easy way out, no easy answer" but that the international community needs to "find something in between doing nothing" and using military force.

As anticipated, Mr. Trump also spoke in harsh terms about Iran and the nuclear deal signed by his predecessor. He called it "one of the worst and most one-sided transactions the U.S. has ever entered" and deemed it an "embarrassment to the U.S."

In an indictment of the international body, Mr. Trump said the Iran nuclear deal provides a "cover for the potential construction of a nuclear program" in the region, an outcome that the U.S. would not tolerate.

"We cannot let a murderer's regime continue these destabilizing activities while building dangerous missiles, and we cannot abide by an agreement if it provides cover for the eventual construction of a nuclear program." It was a signal from the president that he is seriously considering either pulling out of or renegotiating the Iran nuclear deal, CBS News' Margaret Brennan observed. The Iran deal is agreement some of America's strongest allies have signed, and they have said that it cannot be renegotiated.

Mr. Trump also framed his campaign's "America First" ideology as American sovereignty in this speech. He told world leaders that the U.S. "can no longer be taken advantage of" in deals where the U.S. "gets nothing in return."

"In America, the people govern the people rule and the people are sovereign," said Mr. Trump, adding that he was elected to serve the people of his country.

"As long as I hold this office I will defend America's interests above all else but in fulfilling our obligations to our own nations we also realize its in everyone's interest to seek a future where all nations can be sovereign, prosperous and secure," he added.

On Monday, the president kicked off his week of diplomacy with a meeting with Israeli Prime Minister Benjamin Netanyahu, where he promised the leader that there was a "good chance" for peace in the Middle East. He also sat with French President Emmanuel Macron and lauded the president for his impressive military parade on Bastille Day.

Follow Trump's U.N. speech in the updates below:

Trump: "We need to defeat the enemies of humanity"

In his final words to the body, Mr. Trump said, "Our hope is a world of proud independent nations that embrace their duties, seek friendship, respect others and make common cause int he greatest shared interest of all, a future of peace for the people of this wonderful earth."

He says that the true vision and mission of the UN and the message to the world will be that we will "fight together, sacrifice together and stand together" for peace, freedom, justice, family for humanity.

Trump excoriates Venezuelan dictator Nicolas Maduro

"Maduro has inflicted terrible pain and suffering on good people of his country," said Mr. Trump of the dictator.

Mr. Trump calls the unfair election in the region and the starvation of freedom of its people "completely unacceptable and we cannot stand by and watch. We and all other share a goal that goal is to help them regain their freedom recover their country and restore their democracy."

His remark that "the problem is that socialism has been faithfully implemented in Venezuela" receives very little applause or positive reaction from the body.

Trump on unfair cost goals of UN

Powerful people in this room under the guidance of the UN can solve many of these vicious and complex problems," said Mr. Trump, but he noted that the UN "can be a much more accountable and effective advocate for human dignity and freedom around the world."

Trump calls Iran Nuclear Deal an "embarrassment" to U.S.

In harsh tones to the international body, Mr. Trump says the Iran nuclear deal provides a "cover for the potential construction of a nuclear program" in the region.

The president says the U.S. can't abide by an agreement if Iran continues destabilizing activities.

Calling it "one of the worst and one-sided transactions the U.S. has ever entered into", Mr. Trump warns the assembly that "you haven't heard the last on it, believe me."

Trump rails against North Korea, threatens to "destroy" regime

The president calls the North Koreans a "depraved regime" and says they are responsible for the starvation deaths of millions, and for imprisonment torture and oppression of countless more" citing the death of American student Otto Warmbier.

Mr. Trump says their "reckless pursuit of nuclear weapons and ballistic missiles" threatens the entire world with unthinkable loss of human life. He chastised nations would trade or financially support "a country that imperils the world with nuclear conflict."

In a warning to North Korean leaders, whom Mr. Trump called a "band of criminals," he said the U.S. has"great patience" but that America will have no choice but to "totally destroy" North Korea if the regime continues its provocations.

The president referred to dictator Kim Jong Un by a new nickname -- "Rocket man is on a suicide mission for himself and for his regime."

Trump addresses "threats to sovereignty"

"We must protect our nations their interests and their futures. We must reject threats to sovereignty from the Ukraine to the south China Sea," says Mr. Trump, publicly recognizing the global threats posed to the U.S. and abroad.

He adds, "We must uphold respect for law, borders and culture and the peaceful engagement these allow and just as founders of this body intended we must work together and confront together those who threaten us with chaos, turmoil and terror."

Trump: "We can no longer be taken advantage of"

"As long as I hold this office, I will defend America's interest above all else but in fulfilling our obligations to our own nations we also realize its in everyone's interest to seek a future where all nations can be sovereign, prosperous and secure," Mr. Trump says.

He says that "America does more than speak for the values expressed in the UN charter", adding that Americans have paid the "ultimate price to defend our freedom and the freedom of many nations."

Trump on "America First" ideology

"In America, the people govern the people rule and the people are sovereign," says Mr. Trump, saying he was elected to serve the people of his country.

Mr. Trump delivers an "America First" message to the international body, saying, "I will always put America first -- just like you -- as the leaders of your countries will always -- and should -- always put your countries first."

Trump: "Our success depends on a coalition of strong, independent nations"

"We do not expect diverse counties to share the same cultures or system of government but we expect all nations to uphold these sovereign duties, to respect the interests of its own people and rights of every other sovereign nation."

Mr. Trump embraces the idea of "mutual respect" between nations to allow "individuals to flourish in the fullness of the life intended by God."

Trump: "Rogue regimes" threaten nations

"Authoritarian powers seek to collapse the values, the system, and alliance that prevented conflicted and tilted the world toward freedom since WWII," says Mr. Trump of the threats to the international body.

Mr. Trump shifts to addressing poverty and providing a world "free from violence, hated and fear" for children the world over.

Trump tweets ahead of UN speech

President Trump tweets about his "big day" at the United Nations, mentioning "many good things, and some tricky ones, happening."

Big day at the United Nations - many good things, and some tricky ones, happening. We have a great team. Big speech at 10:00 A.M. — Donald J. Trump (@realDonaldTrump) September 19, 2017

While the president writes that his speech will take place at 10:00 AM, Mr. Trump is slated to speak 4th in line in this morning's plenary sessions. Exact timing will depend on how long the leaders before him speak, but he is anticipated to being his address at 10:30 AM ET.