Mr Cook, whose predecessor Sir Malcolm Rifkind would have had to sanction the 1996 assassination attempt, said he had already investigated the claims and had established that they had "no basis in fact".
The Foreign Secretary denied that the Government was poised to sanction an internal investigation by Parliament's all-party Intelligence and Security Committee into the whistle-blowing affair despite growing pressure from the Labour back benches for an inquiry.
Mr Cook's rebuttal came as David Shayler's girlfriend, Annie Machon, repeated his allegations that the assassination attempt was true. She said: "I think they (the Government) are so touchy because they realise what he's saying is true.
"He headed up the Libyan section in MI5 for over two years, so he was very well informed about all matters relating to Libya.
"He also managed to develop a particularly good working relationship with his opposite number in MI6 and I gather that is how he found out the details of the plot to kill Gaddafi," she said.
But in an interview with BBC television yesterday, Mr Cook declared: "The tale about an MI6 plot to assassinate Gaddafi is pure fantasy."
He added: "I have pursued these allegations. I am absolutely satisfied that the previous Foreign Secretary did not authorise any such assassination attempt. I'm perfectly satisfied that SIS (the Secret Intelligence Service - MI6) never put forward any such proposal for an assassination attempt.
"Nor have I seen anything in the 15 months I have been in the job which would suggest that SIS has any interest, any role or any experience over the decades of any such escapade. It is pure fantasy."
Brushing aside Mr Shayler's claims, Mr Cook said: "I do wish people would recognise that ... somebody who has left another service - not SIS, he was never in SIS - is making allegations, no doubt for his own reasons.
"We would like to see him back in Britain in order to pursue those charges that are to be made against him."
He added: "I'm perfectly clear that these allegations have no basis in fact."
John Wadham, Mr Shayler's lawyer and director of Liberty, said: "The Government is saying that this story is not true. If this is what they truly believe, why is my client still in a French jail for disclosing it?"
Mr Shayler is in jail in Paris pending proceedings to get him extradited to Britain to face charges under the Official Secrets Act.
He alleges that a wing of MI6 endorsed a plot to kill Colonel Gaddafi in 1996, but the agents placed explosives under the wrong car when they targeted the Libyan leader's motorcade in February 1996.
The bomb missed Colonel Gaddafi and killed a number of bystanders instead, Mr Shayler has told the New York Times.
Under British law, MI6 can legally carry out acts abroad which would be outlawed in Britain providing they are authorised by the Foreign Secretary.
Mr Shayler fled to France after claiming MI5bungled a number of operations and a government injunction barred newspapers from printing fresh allegations.Reuse content