Donald Trump‘s National Security Adviser John Bolton ended two-days of high-level meetings in Russia – including President Vladimir Putin - with a defiant message: “There’s a new strategic reality.”

The talks were largely dominated by the issue of withdrawal from a Cold War-era arms control treaty, with Mr Bolton also warning officials “don’t mess with American elections”.

The 1987 Intermediate-range Nuclear Forces (INF) treaty was an anachronism of international relations, he told a press conference – “outdated, outmoded and ignored by other countries”. Russia was long in violation of the deal, Mr Bolton said – citing the testing and deployment of a ground-based cruise missile by Moscow. Other countries, like China, Pakistan and India "were not even signatories."

The Kremlin, which denies violations, officially condemned the move and warned that it could lead to a new arms race.

Mr Bolton and Mr Putin emerged from their one and a half hour meeting as they began it – with broad smiles. They cracked jokes in front of the assembled press.

“The US seal depicts an eagle holding 13 arrows and an olive branch with 13 olives,” Mr Putin said. “Did your eagle eat all the olives and now only arrows are left?” Mr Bolton said he had not brought olives.

He seemed to be offering carrots instead.

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There was unexpected agreement that the two presidents would meet – in Paris on 11 November on the sidelines of 100-year celebrations of the end of the First World War. Moscow was genuinely surprised by this possibility. The previous presidential meeting in Helsinki was considered to have been a disastrous experience for the Americans. President Trump’s inability to say whether he trusted his own security agencies over President Putin also damaged the ability of both sides to do business.

Later, when asked at the White House whether he and Mr Putin would meet in Paris, Mr Trump said: “We may.”

“That’s being discussed right now,” Mr Trump said. “I think we probably will. It hasn’t been set up yet, but it probably will be.”

In Moscow, Mr Bolton also left a door open on new sanctions. Under the auspices of the Chemical Weapons proliferation treaty, the Trump administration is obliged to impose a new set of restrictions in November. But there is considerable presidential discretion about how aggressive they can be, right up to major trade restrictions. That has caused worry in Moscow. Mr Bolton said no decision has been made, and even seemed to suggest the US side would not go beyond the bare essentials of “statutory obligations”.

As expected, Mr Bolton issued some tough words on Russian interference in US elections. He said Russia had suffered from its attempts to hack the 2016 presidential election, but, he was keen to point out, that had nothing to do with the eventual outcome – that saw his boss elected. He said the American authorities would be on high alert ahead of the mid-term elections, which take place in early November.

“Don’t mess with American elections,” he warned.

But that was the past. The present was all about cooperation. The two countries had stepped up cooperation on counter-terrorism, Mr Bolton said, and would follow that with work in counter-narcotics and human trafficking. His earlier meetings with the secretary of the security council Nikolai Patrushev, foreign minister Sergei Lavrov and defence minister Sergei Shoigu had been “productive”.

The security advisor also hinted there had been a discussion of a new security architecture with Russia, without giving too many details. The INF treaty was “a bipolar treaty in a multi-polar world”, and this “concerned the Russians substantially”. There was little clarity of what the new architecture could be. There was more clarity about what it wouldn’t be. The advisor offered little prospect of a new, extended treaty to cover emergent nuclear powers.

“We have discussed the conceptual possibility of universalising the treaty since 2004,” he said. “All our efforts failed.”

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Before Mr Bolton’s visit to Moscow, there had been some hope the INF treaty could be saved by further negotiation, especially given that the US had not yet given formal notice. But the advisor put paid to those hopes, confirming the six-month notice would be delivered “in due course”.

One key architect of the treaty has criticised what he described as the short-sightedness of American moves to exit his treaty. In a rare public statement, Mikhail Gorbachev said that “all agreements aimed at nuclear disarmament … need to be preserved for the sake of life on earth”.

The translator and commentator Pavel Palazhchenko was by Mr Gorbachev’s side during negotiations at breakthrough summits in Reykjavik (1986) and Washington (1987), where the INF Treaty was signed. He told The Independent that he did not believe the Trump administration understood the significance of the treaty and had offered bogus arguments about the reasons for withdrawal.

“The talk about other countries possessing intermediate nuclear weapons doesn’t make sense. China, Pakistan and India aren’t going to be attacking the US with these missiles. And I’d doubt there will be many countries who would agree to put American missiles on their soil. So they will be left with the option of basing them in America – with just Mexico and Canada in range.”