Jeremy Corbyn has suggested he is in favour of reducing Nato’s presence on eastern Europe’s borders with Russia and said it was clear the US president-elect, Donald Trump, believed he could improve relations with Vladimir Putin.

The Labour leader said he had “many, many criticisms of Putin, the human rights abuses in Russia and the militarisation of society” but said further escalation had to be avoided.

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“I do think there has to be a process that we try and demilitarise the border between what are now the Nato states and Russia so we drive apart those forces, keep them further apart ... we can’t descend into a new cold war,” he told BBC1’s Andrew Marr show.

The UK is deploying hundreds of troops as well as aircraft and armour to eastern Europe as part of the biggest buildup of Nato forces in the region amid growing tensions with Russia.

Corbyn said the election of Trump, who has expressed scepticism of Nato, was a reflection of the anger communities felt at being left behind by globalisation, but dismissed the suggestion that only the right was managing to capitalise on that feeling.

Bernie Sanders, the leftwing Democrat defeated by Hillary Clinton in the primaries, could have won the election, he said. “There is now a much stronger left movement across the United States and across Europe. Bernie Sanders garnered a very large number of votes,” he said. “Yes, I think he probably could have won.”

The left had become associated with the forces of globalisation during the Obama administration and Labour years in the UK, Corbyn said. “It’s time to move on from the third way, from the New Labour agenda, an agenda which was essentially an incorporation of that free market, economic thinking, which processed deindustrialisation in Britain,” he said.

Corbyn said Trump’s reliance on anti-immigrant rhetoric to make his case for change had infuriated him, and said he wanted to introduce the president-elect to his wife, Laura Alvarez, who is Mexican.

“I’m looking forward to the conversation between my wife and Donald Trump,” he said. “She is a proud Mexican, proud to live here as well, and all of us want to live in a world where we tolerate each other.”

Facebook Twitter Pinterest Jeremy Corbyn and his wife, Laura Alvarez. Photograph: Facundo Arrizabalaga/EPA

The Labour leader said he felt “absolute anger and outrage” over the Republican’s campaign pledge to build a wall between Mexico and the US. “Donald Trump should grow up and recognise the American economy depends on migrant labour.

“I think the treatment of Mexico by the United States, just as much as his absurd and abusive language towards Muslims, is something that has to be challenged and should be challenged.”

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Corbyn suggested he would not make attempts to block any bill to trigger article 50, the two-year-process for leaving the EU, via parliament, and said he was developing contacts across Europe to influence the direction of Brexit.

“I’m already working on potential trade agreements we can make with other countries, the human rights agenda, the environmental agenda and sustainability,” he said. “Those things are very important but I’m also working very hard on an investment strategy for industry and working with many left parties across Europe, who are themselves also opposed to the austerity agenda.”

The former Labour leader Ed Miliband said comparisons could be drawn between Corbyn’s anti-establishment appeal and that of Trump. “Jeremy Corbyn’s trying to win the next general election. I actually think his political outsider status is something that is going to be helpful to him,” Miliband told ITV’s Peston on Sunday.

“His challenge, it was my challenge too, is to get a message across to the country, as he’s successfully done in the Labour party, about what kind of change he wants to bring, how does he want to change the system. Now the challenge we also face in Britain is there are some people who want reassurance, to know Labour can be trusted on the big issues around the economy, but there are some people also who want big change as well and that’s the thing you’ve got to get right.”