AMNA NAWAZ: Overnight, Houthi rebels fired another missile at Israel from their base in Yemen.

The Houthis are labeled by the United States as a foreign terrorist organization supported by Iran.

And, yesterday, President Trump once again demanded Iran cease its support and wrote of the Houthis, "They will be completely annihilated."

Nick Schifrin speaks to a top Houthi official and reports how the Trump administration hopes its new airstrike campaign will succeed where previous ones have failed.

NICK SCHIFRIN: In the Red Sea once again, the U.S. Navy is at war.

For six days, the U.S. has launched dozens of strikes and sorties attacking Houthi targets in Yemen, including for the first time Houthi leadership.

JAMAL AMER, Houthi Foreign Minister (through translator): At the end of the day, we are at war with America.

And, of course, there will be casualties.

But these casualties do not include senior leadership.

NICK SCHIFRIN: Jamal Amer is the Houthi foreign minister.

We spoke to him from the Houthi-controlled Yemeni capital, Sanaa.

JAMAL AMER (through translator): Civilians in Sanaa were bombed because the capital was targeted.

NICK SCHIFRIN: Houthi authorities say the strikes have wounded or killed dozens, including children.

The U.S. denies any civilian casualties and instead blames the Houthis for bringing it on themselves.

Beginning in November 2023, Houthi rebels targeted, seized commercial vessels and kidnapped and killed foreign sailors.

The Houthis claimed to target ships linked to Israel in solidarity with Gaza, but their targets were much wider.

During the Gaza cease-fire, they paused their attacks on ships.

But when Israel blocked humanitarian aid to Gaza, the Houthis vowed to respond.

And, last Saturday, President Trump ordered the new strikes that Secretary of Defense Pete Hegseth told FOX News will continue until the Houthis stop.

PETE HEGSETH, U.S. Defense Secretary: This will continue until you say, we're done shooting at ships, we're done shooting at assets.

NICK SCHIFRIN: Will you stop your targeting of Navy ships and commercial ships?

JAMAL AMER (through translator): When the siege on Gaza ends, the tension in the Red Sea will end.

Therefore, when Gaza receives aid and Israel implements the agreement, everything will end.

NICK SCHIFRIN: Will you expand your attacks to U.S. bases in Djibouti and the United Arab Emirates?

JAMAL AMER (through translator): Now that the USS Truman is targeting Yemen, Truman is being targeted back.

But as the war expands, missiles and aircrafts launched against Yemen will be hit.

NICK SCHIFRIN: The Houthis are an Iranian-backed rebel group that in 2014 seized Sanaa, their enemy, the soldiers of the internationally recognized government of Yemen supported by a Saudi-led coalition that failed to defeat the Houthis with seven years of U.S.-backed airstrikes.

PETE HEGSETH: We don't want a long, limited war in the Middle East.

We don't care what happens in the Yemeni civil war.

This is about stopping the shooting at assets in that critical waterway to reopen freedom of navigation, which is a core national interest of the United States.

And Iran has been enabling the Houthis for far too long.

They better back off.

NICK SCHIFRIN: The U.S. and U.N. say Iran provides the Houthis parts for its advanced missiles, as well as funding, training and intelligence, something the Houthis in Iran deny.

Has Iran asked you to restrain your response to the U.S. strikes?

JAMAL AMER (through translator): Iran doesn't direct Yemen.

Yemen is a sovereign state, and we do not accept directives from anyone.

NICK SCHIFRIN: Iran has had its strategic air defense removed by Israel.

Hezbollah has had its leaders killed and its political influence in Lebanon diminished.

And Hamas itself has had its leaders killed and its military capacity severely diminished.

Do you acknowledge that the so-called Axis of Resistance is at its weakest point in years?

JAMAL AMER (through translator): We are not entirely dependent on our allies.

We merely help our allies.

So this is a Yemeni decision, allies or not.

NICK SCHIFRIN: The Houthis run a de facto government that oversees most of Yemen's population.

Their critics say they govern not for the people, but for themselves, and collect taxes to wage war, despite claims they want peace.

You bombed government ports.

You have refused to recognize the U.N.-backed government.

Until you take that step of recognition, how can anyone take seriously your claim that you want peace?

JAMAL AMER (through translator): The so-called legitimate government is a byproduct of Saudi Arabia, of course.

So we have never spoken to them.

There's always been dialogue and discussion with the kingdom of Saudi Arabia.

NICK SCHIFRIN: But over the last year, the Houthis have arrested dozens of U.N. workers.

One World Food Program employee died in Houthi custody.

Why do you keep detaining U.N. staff?

Many of these people have spent their lives trying to help others, doing humanitarian work.

JAMAL AMER (through translator): Only 23 of the 2,000 Yemeni employees working with international organizations were detained.

Therefore, we confirm that our government will work on strengthening relations with the United Nations.

NICK SCHIFRIN: But the U.S. military says the Houthis seized food from a World Food Program storage depot in Saada.

Why are you doing this when that food is designed for the Yemeni people?

JAMAL AMER (through translator): The food that belongs to the civilians is only taken when there were attacks on Sanaa and the warehouse was threatened.

So we took the food and distributed it to people in need.

NICK SCHIFRIN: And they are in need.

Yemen is one of the world's worst humanitarian crises and now faces a new round of violence that the U.S. hopes can succeed where previous efforts failed to silence the Houthis.

For the "PBS News Hour," I'm Nick Schifrin.