He said she was not an enemy of Libya and was protecting the Libyan Embassy in London when she died, but also insisted that the gunman remained unknown.
In a wide-ranging television interview, speaking in faltering English, he said: "You see, I know that such a thing happened. I know a policewoman was shot and killed when she was doing her duty.
"She is not an enemy to us, and we are sorry all the time and our sympathy, because she was on duty, she was there to protect the Libyan Embassy, but this is the problem that should be solved, but who did it? That is the question."
MPs dismissed Col Gaddafi's apology as "meaningless" and said it could only be taken seriously if he allowed British police to complete their investigation to find Wpc Fletcher's killer.
In the interview with Sky News, the Libyan leader also stated that:
– If Iran develops nuclear weapons it could eventually lead to the Palestinians having nuclear weapons
– President Obama deserved the Nobel Peace Prize, but it was premature and the award revealed "some sort of sycophancy"
– Libyan-British relations were never adversely affected, “even during the time of Lockerbie”.
The Daily Telegraph disclosed recently that British prosecutors were told more than two years ago that they had sufficient evidence to charge two Libyans over the death of Wpc Fletcher.
A senior lawyer carried out an independent review of the case on behalf of the Crown Prosecution Service (CPS) in which he said Matouk Mohammed Matouk and Abdulgader Mohammed Baghdadi could be charged with conspiracy to cause death.
Both men played instrumental roles in organising the shooting at the Libyan embassy in central London, the report said. However, oppositions MPs claim the review was deliberately buried.
Detectives from the Met have made at least three trips to Libya to interview suspects and witnesses. But recent attempts to get back into the country to conclude their investigation have been blocked.
"If Gaddafi has sympathy for the family of Wpc Fletcher, then he should allow the Met to return to Libya and complete their investigation to find her killer," said Tory MP Daniel Kawczynski, chairman of the all-party Libya group.
"It's no good saying sorry and then offering nothing in return. We've heard this all before – a Labour MP went out there and got compensation for the Fletcher family but Gaddafi is still impeding justice.
"He should also put an end to the crass and outrageous agreement that he made with the British Government that the killer, if found, will be tried in Libya. The only way that British justice can be served is if the killer faces trial in a British court.
"These remarks are meaningless. I think that the Fletcher family will only have solace once whoever killed Yvonne is found."
He added that he was infuriated that Col Gaddafi was prepared to do an interview with a journalist while refusing requests to meet he and other British MPs who are trying to improve diplomatic relations with Libya.
Paul McKeever, chairman of Police Federation of England and Wales, welcomed Col Gaddafi’s comments but said the Libyan leader must show further commitment to helping find Wpc Fletcher’s killer.
He said: “It’s a single step on a very long road. As leader of the country he has his hands on the levers of power and we now need him to help get the case progressing and resolve the many unanswered questions.”
Earlier this month, Pc Fletcher's mother, Queenie Fletcher, 76, said she believed the Libyan government was protecting those responsible for her daughter's death.
Referring to Matouk and Baghdadi, she told the Daily Telegraph: "It angers me that these two men have been rewarded with good jobs in the Libyan government when they should be standing trial.
"It is incredibly frustrating to learn that British police found enough evidence more than two years ago to charge two men over our daughter's death, yet nothing has been done."
Col Gaddafi, who was speaking as it emerged that a new police review of the Lockerbie bombing had been launched, also claimed that British oil companies and banks continued to do business with his country even while sanctions were in place because of the terrorist atrocity.
The interview was conducted before the Crown Office in Scotland confirmed that police would look again at some of the evidence in a bid to find the accomplices who carried out the bombing with Abdelbaset Ali Mohmed Al Megrahi.
Prosecutors in Scotland made clear yesterday that they remain convinced of his guilt and said there was no question of reopening the case against him.
But they revealed that police are looking at several “potential lines of inquiry”, including a review of forensic evidence.
The news received a lukewarm reception from British relatives of the Lockerbie victims, most of whom are convinced of Megrahi's innocence and believe that Iran was behind the bombing.
Dr Jim Swire, who lost his daughter Flora, said he would be "livid" if the new inquiry was "just a dodge".
He questioned the usefulness of any inquiry that began by accepting the Libyan's guilt, adding: "Until I get objective evidence that it is going to be a hard hitting and thoroughgoing inquiry I have the greatest difficulty in assuming this is good news.
"I think they are trying to have their cake and eat it. They are not going to question the verdict against Megrahi, but they are launching a new investigation."
He also said it was an "extraordinary coincidence" that the Crown Office had revealed details of the police inquiry on the day that relatives renewed their call to Gordon Brown, the Prime Minister, for a public inquiry.
Pamela Dix, whose brother Peter was killed in the bombing, gave a cautious welcome to the announcement but said it should not be used to replace a full public inquiry.
Meanwhile, ministers in Scotland say the powers of the Scottish Parliament are not wide enough to hold an inquiry with international dimensions, while David Milliband, the Foreign Secretary, insisted that it was purely a matter for the Scottish authorities.
