The row comes after Chinese authorities suddenly returned Ai's passport to him last week -- four years after being confiscated -- opening up the possibility he could travel to London for a major exhibition of his work by Britain's Royal Academy of Arts
Ai, China's most prolific contemporary artist and a prominent dissident, posted an image of the July 29 letter purportedly from the British Embassy in Beijing on his Instagram account.
In it, an immigration official who gives his job title as "Entry Clearance Manager, Beijing," writes that although Ai has applied for a six-month business visit visa, his visa is "restricted to the requested dates of travel on your visa application form, from 9th September 2015 to 29 September 2015."
Explaining the decision, the official says: "It is a matter of public record that you have previously received a criminal conviction in China, and you have not declared this."
A second post on Ai's Instagram account says the decision could mean the artist is unable to attend the installation and opening of his exhibition in London.
Immigration officials say Ai submitted false information in his visa application form and, in conversations, referred to his secret detention in 2011 and accusations of tax evasion, the Instagram post says.
"Ai, who has never been charged or convicted of a crime, attempted to clarify this claim with the UK Visas and Immigration Department and the British Embassy in Beijing over several telephone conversations, but the representatives insisted on the accuracy of their sources and refused to admit any misjudgment," the post says.
"This decision is a denial of Ai Weiwei's rights as an ordinary citizen, and a stand to take the position of those who caused sufferings for human rights defenders."
A representative of the UK Home Office in London said: "Reports that Mr. Ai has been refused a visa are incorrect.
"He has been granted a visa to enable him to travel to the UK for the full duration of the stay he requested."
The Home Office declined to comment further on the case, or to confirm the authenticity of the letter. "All applications are considered on their individual merits and in line with the relevant legislation," it said.
The Ai Weiwei exhibition at the Royal Academy is due to open on September 19 and run until mid-December.
"We're concerned that Ai Weiwei has not been granted a six-month UK visa by the British government," said the gallery's artistic director, Tim Marlow, in a statement.
"We hope for a speedy resolution to this situation and we continue to look forward to welcoming Ai Weiwei at the Royal Academy for his first major institutional exhibition in the UK this September."
A perpetual thorn in the Chinese government's side, Ai was on his way to Hong Kong in April 2011 when authorities took him into custody at Beijing Capital International Airport and detained him for 81 days in a government crackdown on political activists, widely believed to stem from fears of a potential uprising inspired by the Arab Spring
Upon his release on probation in June 2011, Ai faced severe restrictions on his movements
and later accusations of tax evasion -- charges he rejected and unsuccessfully challenged in court
. The government retained his passport.
Last week, after the document's return, Ai posted a photo of himself -- and the passport -- on Instagram for his 121,000 followers.
In an exclusive interview with CNN in Beijing, Ai said,
"My heart is at peace. I feel quite relieved."