AMNA NAWAZ: Welcome to the "News Hour."

The Trump administration is sending more military forces to the Middle East, while at the same time claiming Iran has asked for a cease-fire, a claim Iranian officials say is not true.

Meanwhile, one month into the war, President Trump is scheduled to address the nation later this evening.

He's expected to provide an update on the war effort and reiterate why he believes it was necessary for the United States and Israel to attack Iran.

Nick Schifrin begins our coverage.

NICK SCHIFRIN: In downtown Tehran today, the smoky aftermath of strikes in and near the former U.S.

Embassy that for decades has been controlled by Iranian forces.

And the U.S.

military continued to strike Iran's missiles, drones and defense industrial base.

DONALD TRUMP, President of the United States: We're finishing the job, and I think within maybe two weeks, maybe a couple of days longer, to do the job.

NICK SCHIFRIN: The U.S.

and Israeli strikes have led to the administration's public confidence.

MARCO RUBIO, U.S.

Secretary of State: And we can see the finish line.

It's not today, it's not tomorrow, but it is coming.

(BELL RINGING) NICK SCHIFRIN: The positive rhetoric has rallied the markets and reduced oil prices.

But the reality is more relentless.

For the fifth time today, Israelis headed to their bomb shelters after debris from a shot-down Iranian missile crashed into an apartment outside Tel Aviv, leaving behind a dusty baby stroller and rocker.

Independent researchers say Iran's daily missile launches, while reduced, are still as high as dozens, despite one month of war.

And Iran's stockpile of highly enriched uranium remains inside Iran, even if it's believed buried under nuclear sites attacked by the U.S.

last year.

And the Islamic Revolutionary Guard Corps reiterated today that the Strait of Hormuz remains -- quote -- "firmly and dominantly under its control."

Even modest estimates are that the reduction in oil and liquefied natural gas will stunt many countries' economic growth, International Energy Agency Director Fatih Birol warned today.

FATIH BIROL, Executive Director, International Energy Agency: The loss of oil in April will be twice the loss of oil in March.

On top of that, you have the LNG and others.

So it will come through the inflation.

NICK SCHIFRIN: Given all that reality, today, President Trump reversed previous statements about the strait not being a core issue and wrote on TRUTH Social that Iran asked for a cease-fire and -- quote -- "We will consider when Hormuz Strait is open free and clear.

Until then, we are blasting Iran into oblivion or, as they say, back to the Stone Ages."

Iran's Foreign Ministry denied there were talks at all, as read out by a state TV news anchor.

MAN (through translator): Trump statements about Iran's request for a cease-fire are false and baseless.

NICK SCHIFRIN: And Iranian President Masoud Pezeshkian added in a letter addressed to the American people -- quote -- "Throughout its millennia of proud history, Iran has outlasted many aggressors.

All that remains of them are tarnished names in history."

But, today, President Trump shrugged off Iran's public threats, telling Reuters -- quote -- "I'm dealing with a very good chance that we will make a deal because they don't want to be blasted anymore."

He also said those blasts could resume even after the war ended -- quote -- "I will leave," he said, "and I will take everyone with me.

And if we have to, we will come back to do spot hits."

And he told multiple news outlets he was considering withdrawing the U.S.

from the NATO alliance because it hasn't supported the war in Iran, as Secretary of State Marco Rubio echoed on FOX News last night.

MARCO RUBIO: We are going to have to reexamine whether or not this alliance that has served this country well for a while is still serving that purpose, or has it now become a one-way street, where America is simply in a position to defend Europe, but when we need the help of our allies, they're going to deny us basing rights and they're going to deny us overflight?

NICK SCHIFRIN: But, back in 2023, then-Senator Marco Rubio pushed a bill that was signed by President Biden into law that blocks a president from withdrawing from NATO without two-thirds of the Senate approving, Amna.

AMNA NAWAZ: So, Nick, tell us about the president's address tonight.

What exactly do we expect to hear from him?

NICK SCHIFRIN: A White House official tells my colleague Liz Landers the president is expected to give an operational update on the war and reiterate once again what the administration says has been consistent goals from the beginning of this war, destroying Iran's missile and missile production, its navy, ending support for proxies and ending its ability to have a nuclear weapon once and for all.

As one diplomat told me today, that is the speech that most presidents would have given before the war, because that is essentially a case for the war itself.

And, as we pointed out in our package, the public emphasis from Rubio, from the president on this is that the military operation is succeeding.

And Iran's missile and drone inventory has definitely been reduced and its capacity to have it in the future been reduced.

But the reality is that those missile strikes continue, especially on Israel, as we saw today.

It still has what the president calls nuclear dust, the highly enriched uranium inside Iran, and it now has the stranglehold on the Strait of Hormuz.

AMNA NAWAZ: Speaking of the Strait of Hormuz, you have mentioned there the efforts behind the scenes to try to reopen that critical lane.

What do we know about what's going on?

NICK SCHIFRIN: Yes, so, in public, we have seen the president say, go get your own oil and we might withdraw from NATO because of what the Europeans haven't given us when it comes to this war.

But, in reality, in private, the U.S.

has been coordinating with European countries and the Gulf for an operation that would secure the strait, presumably after the war ends, or at least when a lot of the violence has reduced.

And, as a reminder, this strait is crucial for the world economy; 20 percent of the world's oil and natural gas usually flows through here, but right now it's been largely closed to any tankers other than those that Iran has agreed to let pass.

And so three European officials, one U.S.

official and one regional official tell me tonight that the plan is largely to create a global coalition that would escort tankers, or at least defend tankers, as they go through the British -- as they go through the Persian Gulf.

The British government today announced summits of three dozen countries and senior military officials in the coming days to coordinate that effort.

Now, Amna, this will not be easy.

There are not that many countries that actually have the naval assets to be able to send to the Gulf to do this.

And so these countries tell me that they are certainly hoping that President Trump and the U.S.

would remain in the theater after the war is -- quote -- "over," especially the Marine expeditionary unit, the MEU, that is there right now.

They are capable of, for example, splitting up onto tankers.

You see the Marine expeditionary unit practicing there.

They can sail alongside tankers to help the effort.

They bring enormous capabilities that could help get these tankers through the Gulf.

And alongside those Marines, a U.S.

military official confirms to me tonight that plane, the A-10, could help in this effort, but also help in other efforts if the president chose to escalate this war in the coming weeks.

AMNA NAWAZ: Meanwhile, that Strait of Hormuz is going to be the subject of a Security Council resolution tomorrow.

What does that say?

NICK SCHIFRIN: The idea here is to give international legal authorization for that military effort that I just described.

And according to a text that we obtained today, it says -- quote -- "The resolution authorizes member states acting nationally or through voluntary multinational naval partnerships to use all necessary means, to measure it with the circumstances to secure transit, passage and to deter attempts to close, obstruct or otherwise interfere with international navigation through the Strait of Hormuz."

I'm told by one diplomat on the council, even that language, which has been pared back, is an uphill climb to get to the nine votes they will need for this passage for tomorrow.

But if it is, it would give Europe, it would give the Gulf the legal authorization to have a military operation in the Gulf after the U.S.

and Israel essentially declare the war to be over in order to secure the strait moving forward.

AMNA NAWAZ: Nick Schifrin beginning our coverage tonight.

Nick, thank you.

NICK SCHIFRIN: Thank you.

AMNA NAWAZ: And you can tune in tonight at 9:00 p.m.

Eastern for our special coverage of President Trump's address to the nation on the war with Iran.

You can watch that here on your local PBS station or on our YouTube page or our Web site.