The remarks attributed to the countess about politicians were "selective, distorted and in several cases, flatly untrue".
Two Sunday newspapers said the countess, currently touring the Gulf with her husband the Earl of Wessex, made the comments during a secretly taped conversation with a "bogus sheikh", namely News of the World undercover journalist Mazher Mahmood.
The paper did not publish the story but the Mail on Sunday and Sunday Mirror claimed she had referred to the Queen as the "old dear", Cherie Blair as "absolutely horrid, horrid, horrid" and criticised the prime minister's leadership style as "too presidential".
No official complaint has been made to the Press Complaints Commission by either the countess or Buckingham Palace, a commission spokesman said on Monday.
Buckingham Palace said in a lengthy statement that "not one of the quotes" cited by the Mail on Sunday was accurate.
'Offensive' story
In a series of detailed rebuttals, the statement said it was untrue to claim the countess had "deeply upset the Queen" nor had she been disrespectful to the Queen or the Queen Mother.
The claim she said Prince Charles and Camilla Parker Bowles would marry was also false, it said.
Suggestions that her marriage was imperilled, or that Prince Edward was "furious with her" were untrue, as were references to what Prince Charles might think about her marriage, the Palace statement said.
The remarks attributed to the countess about politicians were "selective, distorted and in several cases, flatly untrue".
The statement said: "A member of the Royal Family such as the Countess of Wessex who is trying to pursue her own career is obviously vulnerable to set-ups such as this.
"And all members of the Royal Family risk tittle-tattle, misinformations and - from time to time - wholesale inaccuracy.
"We suggest no serious journalist gives this story the time of day."
'Reliable' sources
But Mail on Sunday editor Peter Wright said the story came from four different and "reliable" sources.
"There is a tape recording of Sophie's conversation with the fake Arab sheikh.
"If Buckingham Palace are so certain of their version of events, we suggest they publish the recording in full," he said.
The News of the World said it was "disappointed" by "outpourings of disinformation" from rival media jealous of an exclusive interview with the countess in which she spoke out to deny rumours about her husband's sexuality.
Children
The countess told the newspaper: "I can tell you he's not gay...I never believed it."
She told the newspaper she would like to have children. "One of each would be nice."
She added: "I would explore all avenues and I certainly wouldn't rule out IVF."
The Earl and the Countess of Wessex flew to Qatar from Bahrain on Monday as part of a five-day trip to the Gulf to promote British trade.