It only makes sense for the US to continue to pursue the fight against the so-called Islamic State under President-elect Donald Trump, said outgoing Secretary of Defence Ash Carter on Thursday.

"I can't speak for the next administration," Carter reminded reporters during a joint press conference with UK Minister of Defence Michael Fallon in London. However, "it's logical, it makes sense and therefore I expect that logic will recommend itself to the future leadership of the United States," he said, "as it has recommended itself to the current leadership."

Carter added he has "confidence in the future of" the American-led coalition against ISIS, which started in June 2014 and involves 12 foreign governments –including the UK.

"It reflects our common values and the determination of our people to protect themselves and defeat an evil organisation," Carter said. "I would say to my successor... that I expect he will have the same attitude that we do, that is shared by the group in this room today, which is [that] we are constantly looking for ways to accelerate the campaign."

In making nominations for his cabinet, Donald Trump has focused early on defence, quickly picking retired General James Mattis, who headed the United States Central Command from 2010 to 2013 under Obama, as Secretary of Defense. Trump also appointed Michael T Flynn as his national security adviser within days of being elected.

Appearing with Mattis on a North Carolina stage, on 6 December, during his 'thank you' tour, Trump repeated his commitment to building up the US military. He has, however, dropped few hints of what strategy or policies he will pursue as president. Alongside Mattis in North Carolina, Trump made some of his first statements on foreign policy and pledged to, "stop racing to topple foreign regimes we know nothing about" and to "destroy Isis." This suggests he will continue to support the coalition's aims.

Mattis is inclined to take a tougher position toward Iran, and Flynn said during the 2016 US election campaign that he wants the president to take on radical Islamism in a big way. Trump has said he will take a softer approach toward Russia, which is currently fighting forces that oppose the authoritarian government of Bashar al-Assad.

UK Secretary of State for Defense Michael Fallon reminded the UK's allies that "we are dealing here with a global threat" from ISIS terrorism. "I have no doubt that the next US administration will step-up to its traditional role of global leader," he said.