The Trump administration wants the UK to follow the 2016 referendum result and leave the European Union, National Security Advisor John Bolton said.
Speaking to the UK's Telegraph, Mr Bolton said Brexit was an opportunity for the UK to become a "strong and independent country".
His remarks came ahead of a UK visit by President Trump, who has previously stated his support for Brexit.
Mr Trump was critical of Prime Minister Theresa May's negotiations with the EU.
The president's three-day trip, from 3 to 5 June, includes a Buckingham Palace dinner and breakfast with Mrs May, who has hailed the visit as an opportunity for the UK and US "to strengthen our already close relationship".
Speaking ahead of his visit, President Trump praised the UK Conservative Party leadership contender Boris Johnson, saying he would make "excellent" choice.
What did John Bolton say?
In an interview published on Friday, Mr Bolton - a former ambassador to the UN who is considered one of the more hawkish members of the Trump administration - said the world and the Nato military alliance would benefit from the UK being outside the EU.
"As a separate nation again, Britain's impact on the world has the prospect of being even greater... I think it will help us in Nato in particular to have another strong and independent country that will help Nato to be more effective, and that has to be a plus."
He added: "The US preference is for Britain to follow the course of what the people asked for and leave the EU. It's a lesson for everyone in the triumph of democracy."
Mr Bolton said the first step towards a closer relationship was for the next prime minister to finish the Brexit process and negotiate a new trade deal with the US.
Last week, Mrs May - whose withdrawal agreement with the EU was rejected by the UK Parliament three times - announced that she would quit as Conservative party leader on 7 June but stay in office until a successor was found.
"[Mr Trump] wants to make a deal with Britain that will leave both of us better off, and free Britain from the regulatory constraints it faces with the EU," Mr Bolton said.
What has Trump said about Brexit?
The US president, who has previously said Mrs May had not listened to his advice on how to negotiate a deal with the EU, said the agreement reached by the prime minister sounded "like a great deal for the EU".
He had also raised fears that, under Mrs May's Brexit deal, the US and the UK would not be able to negotiate a free trade agreement.
Mr Trump has said he might meet Brexit Party leader Nigel Farage and Conservative MP Boris Johnson - one of the 11 contenders to replace Mrs May as Conservative leader - during his trip to the UK.
Meanwhile, there are growing signs that President Trump will warn British authorities that the US government is prepared to limit intelligence sharing if the UK allows Chinese technology giant Huawei to build part of its 5G network
Washington believes the technology could be used by China to spy, a claim Huawei has denied.
Speaking in Germany, US Secretary of State Mike Pompeo said: "The risk that we'll have to change our behaviour in light of the fact that we can't permit private citizen data from the US or national security data from the US to go across networks that we don't have confidence, that we don't view as trusted networks."
The UK, where 5G was launched in six cities on Thursday, is moving towards letting Huawei build certain parts of its network - non-core elements, such as transmission equipment rather than information infrastructure.