David Lammy has said he told the US vice-president, JD Vance, he was “wrong” to blame the murder of the British teenager Henry Nowak on mass migration.

The deputy prime minister said he spoke to Vance in a phone call on Saturday to tell him “our democratic process is working well” and that he was wrong in his commentary about the murder.

Keir Starmer suggested this week that the US was trying to interfere in British democracy after the senior Republican politician claimed in a post on X that Nowak would be alive “if the last few generations of European elites had stood their ground against the politics of self-hatred and the mass invasion of migrants, many of whom despise the West and the people who love it”.

Lammy told Sunday Morning With Trevor Phillips on Sky News that he warned the vice-president that his post was “not helpful” and that the democratic process in the UK was working well.

Lammy said: “This young man has been convicted. There is an investigation into the police by the independent police complaints authority. There is an investigation into Hampshire police by the inspectorate. The AG is looking at the sentencing in relation to this.

“This has got nothing to do with mass migration. This young man was a Brit. Let’s be … clear about that, and I said, ‘Look, Mr Vice-President, you’re wrong about this,’ and it’s also the case that actually murder is coming down in the United Kingdom.”

On Saturday the US defence secretary, Pete Hegseth, also criticised European countries over migration, for allowing what he described as an “invasion”, during a D-Day anniversary speech in France.

On the 82nd anniversary of the day that allied forces stormed French beaches to liberate Nazi-occupied Europe in 1944, he said: “Sadly, today, different European beaches are stormed by different dangerous ideologies … Beaches in Spain, in Italy, in Greece and Bulgaria. Boats and men arrive. When will European capitals do something about that invasion?”

Lammy was challenged about his own response after Black Lives Matter protests sparked by the death of George Floyd, when he said: “We have to find a way to transform this righteous anger into meaningful reform.”

Lammy rejected the idea that anger was the right response for one death, but not another. “Of course, I’m angry, upset, deeply troubled that this young man has lost his life as a human being. That’s got nothing to look at the colour of his skin. He died horrendously.” But he added that the “right response” was to look at “the action that flows from that”.

Asked about the Vance call by the BBC’s Laura Kuenssberg, he said: “I told him he was wrong.” Asked if he thought Vance was being racist, he said: “I reminded him that the family have called for calm, they don’t want division … I reminded him also of the online space, and how toxic that can become, so that we had a robust conversation, a respectful conversation. We remain colleagues and friends.”

Asked if he believed the police were institutionally racist, he said that he believed the UK had “moved on from that period of institutional racism that was very real in the Stephen Lawrence era”, adding: “I don’t personally recognise that is the appropriate description today”.

Lammy said it was right that police guidance on race was reviewed. “When we look carefully at arrest data, prosecution data, conviction data we do see examples of disproportionality, not just in relation to black communities, Muslim communities, Gypsy Roma, Traveller communities,” he said. “That is not all about racism, some of it can be about socio-economic background and other factors … There’s a level of complexity here, which is why the proper way to deal with this is a considered measured careful review.”