A US ambassador wrote in a secret cable that Prince Andrew spoke “cockily” during an official engagement, leading a discussion that “verged on the rude”.
Tatiana Gfoeller, Washington’s ambassador to Kyrgyzstan, made the remarks in a document revealed by whistle-blower website Wikileaks.
The US has said it “deeply regrets” the leaks, calling them an attack on the international community.
Buckingham Palace has not responded to the reports about Prince Andrew.
In the cable, written in October 2008 and published on the Guardian newspaper’s website, Ms Gfoeller recounts details of a brunch in the Kyrgyzstani capital Bishkek with British and Canadian business people.
Summing the event up, she writes: “Astonishingly candid, the discussion at times verged on the rude (from the British side).”
She said Prince Andrew, who is a UK special representative on trade, criticised the Serious Fraud Office for its probe into a £43bn arms deal between BAE Systems and Saudi Arabia.
Under the sub-heading “Rude language a la British”, she wrote that “he railed at British anti-corruption investigators, who had had the ‘idiocy’ of almost scuttling the Al-Yamama deal with Saudi Arabia”.
She said he also criticised Guardian journalists – “who poke their noses everywhere” – for investigating the deal.
Ms Gfoeller said Prince Andrew told her that the UK, Western Europe and the US were now “back in the thick of playing the Great Game” – a reference to the 19th centrury struggle between the British and Russian Empires for control of Europe.
The Guardian has defended its decision to publish leaked material “More animated than ever, he stated cockily: ‘And this time we aim to win!’ she wrote.
Those at the meeting were discussing potential investment in Kyrgstan, but the ambassador reported that Prince Andrew used the comments of one of the participants to criticise France.
She wrote: “Emboldened, one businessman said that doing business here is ‘like doing business in the Yukon’ in the 19th century, i.e. only those willing to participate in local corrupt practices are able to make any money…
“At this point the Duke of York laughed uproariously, saying that: ‘All of this sounds exactly like France.'”
The Guardian has defended its publication of information from Wikileaks, but the Foreign Office has said that it puts national security at risk.
Despite this, the Foreign Office insisted its relations with Washington would not be damaged and the US ambassador in London, Louis Susman, said he was confident the relationship would remain close.