The contrast in experience between the two men disagreeing over war and theology was striking.

On the one side was Pope Leo XIV, the first North American to head the Catholic church and the first cleric from the Augustinian order, who this week visited the modern Algerian city where Saint Augustine once lived. For Leo, who wrote his doctoral thesis on Augustine’s ideas, it was the culmination of a lifelong intellectual interest.

On the other, the US vice-president, JD Vance, a very recent adult convert to Catholicism with no academic background in the history of the church’s thinking.

At the heart of their disagreement: how Augustine, the fourth-century thinker, framed the idea of a “just war” after centuries in which the early Christian tradition had rejected war and violence, even in self-defence. It is one of the most persistently important ideas in western thinking. Every major philosopher, jurist and theologian on the subject has weighed in on it over the centuries.

The dispute is one strand of the intense controversy caused by the Trump administration’s efforts to imbue the US war against Iran with an incoherent Christian militancy.

At its most bizarre, the US president posted an image of himself on social media as a Christ-like figure healing the sick under flying jets and armed supernatural beings.

The US defence secretary, Pete Hegseth, has meanwhile conducted himself like a modern crusader, claiming the mantle of a righteous violence.

In a series of interventions last month, Leo said Christ’s teaching rejected war and that moreover, he “does not listen to the prayers of those who wage war, but rejects them”.

In recent weeks his discourse has became more pointed. Trump’s threat on 7 April that “a whole civilisation will die tonight” unless Iran made a deal with the US was “truly unacceptable”, he said, adding that such attacks would violate international law.

Vance delivered his reply at an event for the conservative group Turning Point USA at the University of Georgia on 14 April. “When the pope says that God is never on the side of people who wield the sword, there is more than a 1,000-year tradition of just-war theory,” Vance said. “How do you say that God is never on the side of those who wield the sword?” he asked, citing the example of US troops that had liberated France from the Nazis and freed prisoners from the Holocaust camps.

“I think it’s very, very important for the pope to be careful when he talks about matters of theology,” Vance said. “If you’re going to opine on matters of theology, you’ve got to be careful.”

Vance’s attack drew accusations on social media that he was “popesplaining” theology to the pontiff.

Augustine himself had argued that a just war was the business of the state. It could be justified if it was fought with the “right intention” and in pursuit of restoring peace.

The leader who waged war should be like a Christian judge; the innocent should be protected; actions motivated by revenge, wrath or greed invalidated any claim to justice. The tests set by Augustine and the thinkers that followed remain the guiding principles of conflict law.

In an interview with the Catholic Standard in March, Cardinal Robert McElroy of Washington DC said the US and Israeli attack on Iran had failed the just-war criteria. “You cannot satisfy the just war tradition’s criterion of right intention if you do not have a clear intention,” the cardinal said.

Then on Wednesday, Bishop James Massa, the chair of the US Conference of Catholic Bishops’ committee on doctrine, intervened on behalf of the Catholic bishops in the US to make clear that Leo’s comments were not a question of the pope’s “opinion” but Catholic teaching contained in the catechism, the collected doctrine of the church.

“For over 1,000 years, the Catholic church has taught just-war theory, and it is that long tradition the Holy Father carefully references in his comments on war,” Massa said.

“A constant tenet of that 1,000-year tradition is a nation can only legitimately take up the sword ‘in self-defence, once all peace efforts have failed’. That is, to be a just war it must be a defence against another who actively wages war, which is what the Holy Father actually said: ‘He does not listen to the prayers of those who wage war.’”

While many have been offended both by Trump’s posting of himself as Jesus and the attacks on the pope, inevitably, the row has drawn in Trump’s most reliable defenders, including the House speaker, Mike Johnson, who identifies as a Southern Baptist and appears as foggy as Vance about the point Leo was making.

“If you wade into political waters, you should expect some political response,” said Johnson.

Others, such as the conservative Catholic New York Times columnist Ross Douthat, have found themselves straddling the fence, at once complaining that the church can seem hostile to conservatives, while conceding that the Trump administration’s justifications for the war against Iran are ever changing and sometimes evaporating.

“Is the war just or is it not?” asks Douthat, offering his own arguments about why it might be just. “The administration simply has not made a coherent and consistent case for the justice of the conflict.”