Cohen, 35, creator of Ali G, has infuriated the Kazakhstan government with his portrayal of Borat, a bumbling Kazakh TV presenter.
And now a movie of Borat's adventures in the US has caused a diplomatic incident.
The opening scene, which shows Borat lustily kissing his sister goodbye and setting off for America in a car pulled by a horse, had audiences in stitches when it was first shown last week.
But the film, which has just premiered at the Toronto Film Festival, has prompted a swift reaction from the Kazakhstan government, which is launching a PR blitz in the States.
Kazakhstan president Nursultan Nazarbayev is to fly to the US to meet President Bush in the coming weeks and on the agenda will be his country's image.
President Nazarbayev has confirmed his government will buy "educational" TV spots and print advertisements about the "real Kazakhstan" in a bid to save the country's reputation before the film is released in the US in November.
President Nazarbayev will visit the White House and the Bush family compound in Maine when he flies in for talks that will include the fictional character Borat.
But a spokesman for the Kazakhstan Embassy says it is unlikely that President Nazarbayev will find the film funny.
Roman Vassilenko said: "The Government has expressed its displeasure about Borat's representation of our country.
"Our opinion of the character has not changed.
"We understand that the film exposes the hypocrisy that exists both here in the USA and in the UK and understand that Mr Cohen has a right to freedom of speech.
"Nursultan Nazarbayev has taken Mr Bush up on an invitation to visit this country to help build our relationship with the USA.
"I cannot speak for the president himself, only for the government, but I certainly don't think President Nazarbayev and Mr Bush will share a joke about the film.
"The bottom line is we want people to know that he does not represent the true people of Kazakhstan."
The Kazakh government has previously threatened Baron-Cohen with legal action, for allowing Borat to, among other things, make fun of his homeland, demean women, slander gypsies and urge listeners to "Throw the Jew Down the Well."
Anti-Borat hard-liners have pulled the plug on borat.kz, Borat's Kazakhstan-based Website after his frequent displays of anti-Semitism and his portrayal of Kazakh culture.
Nurlan Isin, President of the Association of Kazakh IT Companies took the action after complaints.
He said: "We've done this so he can't badmouth Kazakhstan under the .kz domain name.
"He can go and do whatever he wants at other domains."
The row originally erupted in November 2005, following Borat's hosting of the MTV Europe Music Awards in Lisbon.
The Kazakh Foreign Ministry was furious over Cohen's bad taste representation of the nation.
'No such thing as bad publicity'
Foreign Ministry spokesman Yerzhan Ashykbayev told a news conference: "We view Mr. Cohen's behaviour at the MTV Europe Music Awards as utterly unacceptable, being a concoction of bad taste and ill manners which is completely incompatible with the ethics and civilized behaviour of Kazakhstan's people.
"We reserve the right to any legal action to prevent new pranks of the kind."
Baron Cohen responded to Ashykbayev in character by posting a video on the Official Borat website.
In the video, Borat said, "In response to Mr. Ashykbayev's comments, I'd like to state I have no connection with Mr. Cohen and fully support my Government's decision to sue this Jew.
"Since the 2003 Tuleyakiv reforms, Kazakhstan is as civilized as any other country in the world.
"Women can now travel on inside of bus, homosexuals no longer have to wear blue hats, and age of consent has been raised to eight years old."
His blatant outpouring then prompted the Kazakh government to hire two public relations firms to counter the claims, and ran a four-page advertisement in The New York Times.
The ad carried testimonials about the nation's democracy, education system and the power and influence enjoyed by women. News of President Nazarbayev's upcoming visit has prompted experts to study the character's impact on US culture.
Sean R. Roberts, Central Asian Affairs Fellow at Georgetown University, has been studying the phenomenon.
He said: "I have found that more Americans are aware of Kazakhstan than four years ago when I last lived in the United States.
"The increased knowledge of Kazakhstan, however, is not due to the country's economic successes or its role as a U.S. ally in the war on terror.
"Instead, most Americans who have heard of Kazakhstan have heard of it through a satire of a Kazakh journalist named Borat.
"Borat certainly does not promote an image of Kazakhstan that is in sync with that which the government and its leader would like to promote abroad.
"As the old adage goes, however, 'there is no such thing as bad publicity.'
"If that is true, Borat is bringing much more publicity to Kazakhstan."
Cohen's representatives refused to allow him or his alter ego to respond to the controversy because it's not close enough to the film's release date.