AMNA NAWAZ: President Trump is openly condemning the head of the Roman Catholic Church after Pope Leo XIV criticized the U.S.

and Israeli war with Iran.

William Brangham reports on the rare public battle between the president of the United States and the first U.S.-born pope.

WILLIAM BRANGHAM: After his attacks on Pope Leo earned him global condemnation, the president this afternoon refused to relent.

DONALD TRUMP, President of the United States: We believe strongly in law and order, and he seemed to have a problem with that, so there's nothing to apologize for.

He's wrong.

WILLIAM BRANGHAM: The president's remarks today doubled down on his lengthy tirade online and on the tarmac last night.

DONALD TRUMP: He's a very liberal person, and he's a man that doesn't believe in stopping crime.

He's a man that doesn't think that we should be going with a country that wants a nuclear weapon so they can blow up the world.

I'm not a fan of Pope Leo.

WILLIAM BRANGHAM: The president spoke yesterday after returning to Washington from Florida.

Echoing his post on social media, where he took issue with Pope Leo's criticism of American actions in Venezuela and Iran, he wrote -- quote -- "I don't want a pope who criticizes the president of the United States, because I'm doing exactly what I was elected in a landslide to do."

The president also implied that the first ever American pope owed his job to Trump, writing: "If I wasn't in the White House, Leo wouldn't be in the Vatican."

Today, en route to Algeria, Pope Leo responded.

POPE LEO XIV, Leader of Catholic Church: I have no fear neither of the Trump administration, nor speaking out loudly about the message of the Gospel.

And that's what I believe I am called to do.

WILLIAM BRANGHAM: The pontiff defended his earlier comments about the evils of war.

POPE LEO XIV: I basically said that the message of the church, my message, the message of the Gospel, blessed are the peacemakers.

I do not look at my role as being political, a politician.

I don't want to get into a debate with him.

I don't think that the message of the Gospel is meant to be abused in the way that some people are doing.

And I will continue to speak about this, against war, looking to promote peace, promoting dialogue and multilateral relationships among the states to look for just solutions to the problems.

WILLIAM BRANGHAM: It was Pope Leo's comments two days ago that apparently sparked the president's anger.

At a special prayer vigil Saturday night at St.

Peter's Basilica, Leo denounced the -- quote -- "delusion of omnipotence" that he argued was fueling the war in Iran and other global conflicts.

POPE LEO XIV (through translator): May the madness of war cease and the Earth be cared for and cultivated by those who still know how to create, safeguard and love life.

WILLIAM BRANGHAM: Today, the president's comments about the pope drew widespread criticism.

Catholic Bishop Robert Barron, who leads the Diocese of Winona-Rochester in Minnesota and serves on the White House's Religious Liberty Commission, wrote: "The statements made by President Trump on TRUTH Social regarding the pope were entirely inappropriate and disrespectful.

I think the president owes the pope an apology."

The head of the U.S.

Conference of Catholic Bishops, Archbishop Paul Coakley, also issued a statement -- quote -- "I am disheartened that the president chose to write such disparaging words about the Holy Father.

Pope Leo is not his rival, nor is the pope a politician.

He is the vicar of Christ, who speaks from the truth of the Gospel and for the care of souls."

President Trump stoked more outrage when he posted this Christlike image of himself, hands glowing and healing a sick man.

When even some allies condemned the image as blasphemy, the president took it down, saying it had been misconstrued.

DONALD TRUMP: It was me.

I did post it.

And I thought it was me as a doctor and had to do with Red Cross.

There's a Red Cross worker there, which we support.

And only the fake news could come up with that one.

WILLIAM BRANGHAM: President Trump's relationship was also tense with Pope Leo's predecessor, Pope Francis.

They clashed at times over immigration and climate change.

After Francis died, the president posted another A.I.-generated image, this one of himself wearing papal robes.

Meanwhile, after landing in Algeria today... POPE LEO XIV: In this place, let us remember that God desires peace for every nation.

WILLIAM BRANGHAM: ... Pope Leo laid a wreath at the monument honoring those who died in that nation's war for independence and said a prayer for peace.

For the "PBS News Hour," I'm William Brangham.