The intervention, coming just days before David Cameron's keynote speech on Europe – supposedly set for January 21 in the Netherlands – appears to be a warning that any UK withdrawal from the EU would damage the special relationship.
At a briefing with Westminster journalists, Philip Gordon, the US's Assistant Secretary of State for European Affairs, said: "We have a growing relationship with the EU as an institution, which has an increasing voice in the world, and we want to see a strong British voice in that EU. That is in America's interests. We welcome an outward-looking EU with Britain in it."
Tory Eurosceptics have already warned Mr Cameron's leadership would be under threat if he does not promise an in-out referendum shortly after the next General Election.
The PM has promised a chance for Britons to give their fresh consent on a new settlement once the way ahead for the eurozone is clearer, but he has stressed he is not personally in favour of an in-out poll.
Mr Gordon said "referendums have often turned countries inward". He added: "Every hour spent debating the institutional make-up of the European Union is one hour less spent on how to deal with the common issues of jobs, growth and international peace around the world."
His intervention came as British business leaders, including Virgin's Sir Richard Branson, warned of the uncertainty that could be created by demands for a new relationship with the EU.
A No 10 spokesman said: "The US wants an outward-looking EU with Britain in it. So do we."
However, Douglas Alexander, the shadow foreign secretary, noted: "There is a real risk of Britain sleepwalking towards exit because of a Prime Minister motivated more by the need for party unity than by the interests of the country."
Meanwhile, EU leaders have told Mr Cameron the eurozone can repair itself under the existing Lisbon Treaty, meaning the PM could be deprived of the chance to agree a new settlement with Brussels and bring back powers to Britain.