Going one up on George W. Bush's three-strong "axis of evil", US President Donald Trump went after a four-strong "small group of rogue regimes" in his first speech to the UN General Assembly on Tuesday - a contradictory demand for patriotism and sovereignty for all nations that would be policed by his administration, the inward rhetoric of his campaign notwithstanding.

If he had to, Trump would totally destroy North Korea: "Rocket Man [Kim Jong-un] is on a suicide mission for himself and for his regime."

The Iran nuclear deal was an embarrassment to the US: "And I don't think you have heard the last of it - believe me."

If need be, he'd sort out Venezuela: "We cannot stand by and watch."

And Cuba, too, was put on notice: "We'll not lift sanctions on the Cuban government until it makes fundamental reforms."

The first push-back came from French President Emmanuel Macron, who said the Iran deal was "solid, robust and verifiable - [renouncing it would be] a "grave error".

On North Korea: "France rejects escalation and will not close any door to dialogue."

And on the Paris climate accord, France and the rest of the world were getting on with the business - without the US.

And, on Wednesday, Trump's Secretary of State Rex Tillerson is expected to confront a brick wall of opposition to a push by the US, egged on by Israeli Prime Minister Benjamin Netanyahu, to pick apart the Iran deal, when he meets the other signatories to the 2015 agreement: China, Russia, France, Britain, Germany and the European Union.

Speaking to an audience accustomed to hearing the likes of Moscow and Beijing deflect criticism by invoking "sovereignty", Trump used the word more than 20 times, as he observed that some parts of the world were "going to hell" - but many of its problems could be fixed by a good dose of his "Make America Great Again" ethos and by every nation embracing its own nationalism.

But the speech was silent on the complexity of differing national sovereign interests - say Russia and China on the North Korea crisis; or the very different position of much of Europe, on the one hand, and Israeli and the Sunni Arab world, on the other, on the Iran nuclear deal.

As it was on the human rights record of allies such as Saudi Arabia; and on countries that don't register on Trump's radar - such as Myanmar, which the UN is accusing of running a "textbook" example of ethnic cleansing against its Muslim minority.

"As President of the US, I will always put America first, just like you, as the leaders of your countries, will always and should always put your countries first," Trump said, to one of a few, if muted, rounds of applause, in the course of his speech.

"The United States will forever be a great friend to the world, and especially to its allies.

"But we can no longer be taken advantage of or enter into a one-sided deal where the US gets nothing in return. As long as I hold this office, I will defend America's interest above all else. But in fulfilling our obligations to our own nations, we also realise that it's in everyone's interest to seek a future where all nations can be sovereign, prosperous and secure."

Searching for historical anchors, Trump harked back to the presidency of Harry Truman, the Marshall Plan and the restoration of Europe, but Trump's America sounded small and less troubled by how others fared; others would have to pick up the tab and he'd not be signing on for "one-sided" deals.

Challenging his audience of leaders, Trump posed what he said was a true, basic question for the UN and for people worldwide: "Are will still patriots? Do we love our nations enough to protect their sovereignty and take ownerships of their future?"

Trump congratulated Moscow and Beijing for their Security Council votes to tighten sanctions on Pyongyang.

Interestingly, he took just a glancing blow at Russia over its annexation of Crimea from Ukraine, perhaps the worst current breach of a nation's sovereignty; and said nothing of the breach of American sovereignty by Moscow's meddling in the 2016 US elections.

And he did not name China for its continuing trade with North Korea, when he said: "It is an outrage that some nations would not only trade with such a regime, but would arm, supply and financially support a country that imperils the world with nuclear conflict."

When it came to naming and shaming the Communist villains of the world, Trump was silent on China and took a historic swipe at Moscow, as he tore into Venezuela and Cuba.

"From the Soviet Union to Cuba to Venezuela, wherever true socialism or communism has been adopted, it has delivered anguish and devastation and failure," he said, adding that, in pledging not to lift sanctions on Havana, his administration had "stood against the corrupt, destabilising regime in Cuba".

There was little applause when Trump declared: "If the righteous many do not confront the wicked few, then evil will triumph. When decent people and nations become bystanders to history, the forces of destruction only gather power and strength."

Neither Iranian President Hassan Rouhani nor his foreign minister Mohammad Javad Zarif were in the chamber as Trump railed against Tehran's "murderous regime", claiming: "It is far past time for the nations of the world to confront another reckless regime - the Iranian government masks a corrupt dictatorship behind the false guise of a democracy."

But earlier in the day, Rouhani insisted that Iran had complied fully with the terms of the nuclear deal, warning that the US would be the loser if it walked away. "The US is therefore a country that cannot be trusted - we will be the winners," he said.

North Korea's UN ambassador made a deliberate show of quitting the chamber before Trump spoke.

And if UN Secretary General Antonio Guterres was at one with Trump's critique of the UN on Monday, on Tuesday he had a sober lecture for the US President - at the same time as he rebuked Washington implicitly - on climate change ("the science is unassailable") and on refugees ("closed doors and open hostility").

"No one is winning today's wars - from Syria to Yemen, from South Sudan to the Sahel, Afghanistan and elsewhere, only political solutions can bring peace.

"We should have no illusions. We will not be able to eradicate terrorism if we do not resolve the conflicts that are creating the disorder within which violent extremists flourish. Only that unity can lead to the denuclearisation of the Korean Peninsula and - as the resolution recognises - create an opportunity for diplomatic engagement to resolve the crisis.

"When tensions rise, so does the chance of miscalculation. Fiery talk can lead to fatal misunderstandings. The solution must be political. This is a time for statesmanship.

"We must not sleepwalk our way into war."

Vali Nasr, dean of the Johns Hopkins School of Advanced International Studies, was unsettled when he spoke to reporters, saying: "It looks like we'll respect the sovereignty of countries we like, whether they are dictatorships or democracies, but we will not respect the sovereignty of countries we don't like. His [Trump's] definition of sovereignty comes from a very narrow domestic prism."

And as reporters and analysts laboured to shoehorn the speech into a Trump Doctrine format, Aaron David Miller, a former US peace negotiator now attached to the Woodrow Wilson International Centre for Scholars, marked it down as Trump "awkwardly trying to reconcile" his America First nationalism with the globally-minded UN.

"President Trump's speech was a confusing hodgepodge of tropes, themes and threats that made one unmistakable point: there is no coherent Trump Doctrine," he said.