GEOFF BENNETT: Welcome to the "News Hour."

President Trump took his America first foreign policy to the world stage today, using his address to the U.N.

General Assembly to defend the war with Iran and issue a stark warning to Iran's leadership.

Mr.

Trump said a deal could come after the midterm elections, and that the alternative was to -- quote - - "annihilate the Islamic Republic."

The president's speech and several of his meetings today were broadcast by the U.N.

's TV operation, which is separate from the U.S.

pool of TV networks that is suing the president over his ban of three news organizations.

Nick Schifrin starts our coverage from New York.

NICK SCHIFRIN: Today, in front of global leaders whose countries have been hit by unprecedented attacks, food shortages and higher energy prices because of the U.S.

Israeli war in Iran, President Trump defended his decision to go to war.

DONALD TRUMP, President of the United States: They were the bully of the Middle East, but they're the bully no more.

NICK SCHIFRIN: And at the U.N., whose charter bans countries from threatening military force except in self-defense, President Trump delivered a threat.

DONALD TRUMP: Will a deal be made with Iran that lets them rebuild and create a far greater country than it ever was before, or do I annihilate the Islamic Republic, and do it quickly, never giving them a chance to kill and destroy people and countries again?

Do I drive them into hell with no chance of survival and no hope of future greatness or generations?

But I believe we will make a deal right after the election, because it doesn't make sense for them not to.

NICK SCHIFRIN: For his part today, Iranian President Masoud Pezeshkian said Iran did not trust another negotiation, even though Foreign Minister Abbas Araghchi met today with U.S.

negotiators Steve Witkoff and Jared Kushner.

MASOUD PEZESHKIAN, Iranian President (through translator): We have been at the negotiating table several times.

The whole world sees that they are easily trample on, the agreements.

They cannot use force to compel people to submit.

NICK SCHIFRIN: But President Trump's threats of force against a NATO treaty ally led to today's agreement between the U.S., Denmark, and Greenland, which has been part of the Kingdom of Denmark since 1721.

The deal allows the U.S.

to add to its existing military presence with two new bases.

NATO will boost presence in the Arctic, and the world's largest island will permanently ban Chinese and Russian investment without giving up Greenland or Danish sovereignty.

DONALD TRUMP: We're going to have a tremendous relationship, a secure relationship, and we look forward to it.

NICK SCHIFRIN: That's a turnaround from his previous threats disrespecting Danish sovereignty that threatened overall NATO cohesion.

DONALD TRUMP: And all we're asking for is to get Greenland, including right, title and ownership, because you need the ownership to defend it.

You can't defend it on a lease.

NICK SCHIFRIN: But, today, Denmark and Greenland call this deal a win-win.

METTE FREDERIKSEN, Prime Minister of Denmark: The, day we are signing an even bigger and better agreement, a deal that can last forever.

This deal is good for the United States.

It's good for Greenland, for Denmark, for the NATO alliance, and therefore also good for Europe.

JENS-FREDERIK NIELSEN, Prime Minister of Greenland: This is not only an agreement about us, it is an agreement with us.

It takes into account the people of Greenland, our rights, our livelihoods, and the development of our country.

NICK SCHIFRIN: President Trump also met with Middle Eastern allies as the conflict with Iran has spread, this strike by the Iranian-backed Houthis on a public market in Yemen.

The Houthis are trying to expand their assault after seizing the Red Sea coast along the Bab al-Mandab Strait.

Regional officials are concerned the Houthi campaign gives Iran even more leverage, combining choke holds over both the Bab al-Mandab and the Strait of Hormuz.

The Houthis have also damaged a critical Saudi pipeline that the kingdom signaled today it's close to restarting.

DONALD TRUMP: Together, we're on the verge of overcoming challenges that have plagued this region for decades.

This has gone on for decades.

NICK SCHIFRIN: The president's positivity left it to outgoing Secretary General Antonio Guterres to acknowledge a world that feels fractured.

ANTONIO GUTERRES, United Nations Secretary-General: The fault lines in our world are widening.

Cracks have become canyons.

NICK SCHIFRIN: Today was Guterres' final U.N.

General Assembly speech after a decade in office.

He said challenges from climate change to AI require an interdependent world to avoid fragmentation and free-for-all.

ANTONIO GUTERRES: Building a networked future begins with the recognition, especially by superpowers that their power isn't so super, and governments with the greatest AI capabilities have the greatest responsibilities to humanity to establish channels for dialogue, transparency, trust, and cooperation, not despite geopolitical rivalry, but precisely because of it.

MARIA RESSA, CEO, Rappler: We cannot just keep raising the alarm.

We have to act.

NICK SCHIFRIN: A U.N.

independent panel also warned in a new report about AI threats.

But if the world came here hoping Washington would rein in AI, President Trump made clear it wouldn't be him.

DONALD TRUMP: The very same people who said we will all be dead in 12 years because of global warming, these are the same people that are now saying that AI is going to kill us all, that robots are going to attack us, and that everything is going to be a total disaster.

So we're going to encourage it, not rein it in.

NICK SCHIFRIN: And, tomorrow, the Security Council will hold a meeting about artificial intelligence with foreign ministers with addresses by both American and Chinese AI leaders -- Geoff.

GEOFF BENNETT: And, Nick, beyond what you have laid out in your report, the president today also offered his vision for Latin America?

What is it?

NICK SCHIFRIN: One in which the U.S.

has unvarnished military, economic, and diplomatic power.

Today, he said that the drug cartels across the region were -- quote -- "the ISIS of the Western Hemisphere."

He predicted also that Cuba will fall.

U.S.

officials tell me that there's a race between the U.S.

and Cuba.

The U.S.

is trying to impose enough pressure on Cuba to open up economically, to change politically, while Cuba is trying to wait out, to outlast President Trump.

And, tonight, President Trump will meet with Venezuelan acting President Delcy Rodriguez.

Today, the president was unabashed about the U.S.

exporting Venezuela to the U.S., despite the Geneva Convention explicitly prohibiting nations from using war to -- quote -- "pillage the country's economic resources."

DONALD TRUMP: It was a war, but it's perhaps the biggest deal ever made.

To the victor belong the spoils.

GEOFF BENNETT: And, Nick, shifting our focus back to Yemen now, what are officials telling you about how the Houthis can be stopped?

And you have some new reporting?

NICK SCHIFRIN: Yes, Geoff, it's a really big challenge.

The Houthis have recently swept through the Red Sea coast right along the Bab al-Mandab.

And anti-Houthi forces, including the Yemeni government, the internationally recognized Yemeni government, didn't put up much of a fight.

The Saudis have launched airstrikes on the Houthis, but they have not been effective.

And now the Houthis are trying to expand their control further east.

A senior U.S.

official tells me that President Trump is determined not to launch U.S.

airstrikes on the Houthis, despite a request to do so by Saudi Crown Prince Mohammed bin Salman, although, late last week, he did order the military to do an assessment about U.S.

airstrikes, leading some in the military to suggest that they thought airstrikes were imminent.

But the senior U.S.

official tells me that, no, that was just an assessment and that there are no U.S.

airstrikes on the Houthis on the table.

The U.S.

and the Houthis still have a deal, Geoff, in which the U.S.

has agreed not to attack the Houthis, and the Houthis have agreed not to attack U.S.

warships or any other ships in the Red Sea, with the exception of those strikes and threats against Saudi tankers in the area.

Meanwhile, a U.S.

senior official tells me that they would like to see Saudi Arabia make a deal with the Houthis.

The Houthis have been asking for restrictions on their airport and their flights lifted.

They have been asking for billions in cash in unpaid salaries and oil compensation.

And they have also been asking for political recognition.

That is not a list, Geoff, that the Saudis have been interested in giving in to.

But analysts say the Houthis think they're winning.

They're not about to give in or compromise at all on their side as well.

And so that leads to this very difficult, problem, Geoff, without a clear solution.

GEOFF BENNETT: Nick Schifrin reporting tonight from the U.N.

Nick, our thanks to you, as always.

NICK SCHIFRIN: Thank you.