One of Keir Starmer’s senior ministers has dismissed suggestions by Donald Trump that the British government call out the military to help deal with irregular migration.

Peter Kyle, the UK business secretary, brushed off the comments, which the US president made on Thursday at the end of his two-day state visit.

Trump told a press conference at Chequers: “You have people coming in and I told the prime minister I would stop it, and it doesn’t matter if you call out the military, it doesn’t matter what means you use.”

Kyle said on Friday, however, the government did not need to call on the armed forces to deal with small boat crossings, hours after the UK successfully deported a second asylum seeker to France under the “one-in, one-out” pilot scheme.

He told BBC Breakfast: “What [Trump] suggested was that the military are used, but we have the UK Border Force. It is now established and has been reinforced and bolstered, and has new powers under this government.

“The navy actually does have a working relationship with the UK Border Force, and the navy can be called upon if needed. So we do have the functional relationship that we need within our military and keeping our borders safe and secure.

Peter Kyle: ‘We are successfully able to begin the deportations and the returns to France.’ Photograph: Jordan Pettitt/Reuters

“What we really need at the moment is our military focus on all of those really key issues around the world [that] are directly relating to our national defence.”

Kyle was speaking after an Eritrean man became the second person to be flown to France under the new deportation scheme, under which the government will deport up to 50 people a week in return for accepting the same number of others.

The government has been thwarted in its attempts to deport other people after last-minute legal challenges.

Kyle said: “We are making sure that we are getting as many people who don’t have the right to be here returned as swiftly as possible. There’s a lot of cases going through the courts at the moment. As you can see, we are successfully able to begin the deportations and the returns to France.”

Trump has left the UK after his unprecedented second state visit. The president largely avoided causing controversy during a 90-minute press conference on Thursday, despite attracting attention for his comments on migration.

But while British officials were pleased with the outcome of the visit, they have failed to secure one of their main priorities – a reduction in the 25% tariffs that the US charges on British steel products.

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Officials say privately that they do not expect those tariffs to come down in the foreseeable future, but Kyle said on Friday that negotiations between the two countries would continue.

“The president also said – because I was there in the room when he said it yesterday – that the talks on steel and other areas will continue into the future,” he added.

He also defended his previous comments that Peter Mandelson had been appointed as ambassador to the US because of his “talents”. Mandelson was sacked days before the trip after details emerged about his former friendship with the child sex offender Jeffrey Epstein.

“Nobody is appointed to becoming ambassador to a great country, on behalf of our country, unless you have talents,” Kyle said. But he added: “Let me be really clear about this, I do not defend any of the actions that Peter Mandelson took in his relationship with Jeffrey Epstein. Absolutely not.”

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