Abdelbaset Ali Mohmet al-Megrahi, the only person convicted over the 1988 Lockerbie bombing which killed 270 people, died almost three years after being freed from jail on compassionate grounds.
"He died an hour ago," his brother Abdelhakim al-Megrahi told AFP, putting the time of death at shortly after 1 pm (1100 GMT).
A Scottish court sitting in the Netherlands convicted Megrahi in 2001 of the bombing of Pan Am flight 103 over the Scottish town of Lockerbie, which killed all 259 people on board along with 11 people on the ground.
Most of the passengers on the Boeing 747 jet headed from London to New York were Americans.
Megrahi, 60, who suffered from prostate cancer, was released on compassionate grounds in 2009 after doctors said he had only three months to live.
His death on Sunday prompted sharply contrasting reactions.
The US government, which was outraged by Scotland's decision to free the former Libyan airline security chief, said his death ended an "unfortunate chapter."
British Prime Minister David Cameron, meanwhile, said the Libyan should never have been released from prison and rejected calls for an inquiry into his conviction.
"Megrahi's death concludes an unfortunate chapter following his release from prison in 2009 on medical grounds -- a move we strongly opposed," said US National Security Council spokesman Tommy Vietor.
"We will continue working with our new partners in Libya toward a full accounting of Kadhafi's horrific acts," he added.
Britain's newspapers believe that his initial conviction by a Scottish court in 2001 was flawed and called for an official probe.
"With so many loose ends remaining and so many questions about the original trial unresolved, the Scottish government should agree to a public inquiry into the tragedy," said the left-leaning Independent's editorial.
"Megrahi's death is no reason to stop trying to get to the truth," it added.
Megrahi had always maintained his innocence, arguing that US agencies "led the way" in securing his conviction, and his brother Abdelhakim defended him on Sunday, saying he was the "scapegoat" of Moamer Kadhafi's regime.
"He has died and has left us with the feeling of injustice," he told AFP. "Everyone knows that the Kadhafi regime blamed its mistakes on others."
Another brother, Mohammad al-Megrahi, too insisted Abdelbaset was innocent.
"All the darkness of the universe will never cover the flame of the candle which is the truth," he said, speaking outside the family home where relatives had gathered to receive condolences.
Some have suggested the decision to allow Megrahi to return to Libya was taken to smooth the way for lucrative oil deals struck by British firms.
Scotland's First Minister Alex Salmond argued that Megrahi's death vindicated his administration -- which can make decisions on justice matters independently of the British government.
His death "puts to rest some of the conspiracy theories which have attempted to suggest that his illness was somehow manufactured -- today's news confirms what we have always said about his medical condition", Salmond said.
The convict had been greeted as a hero on his return to Kadhafi's Libya, after having served eight years of a minimum 27-year sentence for his role in the Lockerbie bombing.
The fact that he survived much longer than the doctors had estimated provoked indignation in Britain and the United States.
On Sunday, the British premier said Megrahi's death was a day to remember "the 270 people who lost their lives in what was an appalling terrorist act."
Cameron added: "I've always been clear he should never have been released from prison."
He also dismissed calls for an inquiry into his conviction.
"There was a proper process, a proper court proceeding and all the rest of it. We have to give people the chance to mourn those that were lost. I'm very clear that the court case was properly done and properly dealt with."
But the father of one of the victims of the Lockerbie bombing, who has long believed Megrahi was innocent, said it was a sad day.
"It is a sad time, I think. I have been satisfied for some years that this man was nothing to do with the murder of my daughter," Jim Swire, whose daughter Flora was killed in the attack, told BBC TV.
"I think Scotland has a big question to answer as to why his verdict hasn't long since been reviewed."
Swire said Megrahi had been in great pain when he visited him in Tripoli in December, and that he thought it would be their last meeting.
"He was in a lot of pain, and his demise now has at least relieved his pain for him," Swire said.
"So from now on perhaps we can concentrate on trying to find out who did murder my daughter and all those other people."
Swire, a member of the Justice for Megrahi (JFM) group, said he was confident that the guilty verdict passed on Megrahi by a Scottish court sitting in The Netherlands in 2001 would be overturned.
But several relatives of US citizens killed in the Lockerbie bombing said on Sunday they were pleased that Megrahi had died.
"He deserved to die," said Susan Cohen, whose daughter Theodora was one of the victims.
"He was a mass murderer. I feel no pity around him. He got to die with his family around him. My daughter, at age 20, died a brutal, horrible death," she told CNN.
In December, Megrahi told several British newspapers in what was billed as a "final interview" that a book being written by investigative journalist John Ashton would clear his name.
"I am an innocent man," he told the papers, including The Times and the Daily Mail.
"I am about to die and I ask now to be left in peace with my family," he said.
Megrahi's funeral was due to take place on Monday afternoon, Libya's Lana news agency quoted one of his sisters as saying.
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