Tyler Gosnell, Managing Director of International Inbound Travel at the trade body, told the Visit USA general meeting in London the US was "losing market share" to rival destinations, although British demand remained resilient.
"I wouldn't describe it as the golden age of international inbound travel for the United States at the moment," he said.
"America was the only major country where international inbound travel declined last year, about 5%, while international arrivals globally grew at approximately 5%. America is losing market share."
However, Gosnell highlighted the UK as a standout performer, with visitor numbers forecast to rise by around 3.5% this year to 4.2 million trips.
"The UK has been a resilient market," he said, describing Britain as the US's "number one overseas source market".
Destinations including Japan, South Africa, Canada and countries in the Middle East were investing aggressively to attract international visitors, he said.
"The US continues to lose market share, and capturing that market share back is incredibly difficult," he said. "These other countries are investing more, they're competing harder and they're aligning strategically across their nations."
Gosnell acknowledged some consumers were concerned around the cost of visiting the US, over areas including visa fees, national park charges, resort fees and tipping confusion.
"We've been known as the land of the free, and now being known as the land of the fee, which is not a good place," he said.
Despite the challenges, he said major events – including this summer's Fifa World Cup – had boosted sentiment towards the destination, with the association’s own research showing traveller intent to visit the US in the next two years rising 5% during the tournament.
Visit USA UK is the largest US tourism association in the world with more than 200 members.
The meeting also heard how the association’s new advocacy sub-committee, chaired by Brendan Croft, is aiming to work more closely with organisations including the US Travel Association and the International Inbound Travel Association to drive more tourism to the US.