A Scottish government spokesman said the decision was reached following proper procedures.
"The justice secretary reached his conclusions on the basis of Scotland's due process, clear evidence, and the recommendations from the parole board and prison governor," the spokesman said.
"Compassionate release is not part of the US justice system but it is part of Scotland's," he added.
"Mr MacAskill could not have consulted more widely -- he spoke with the US families, the US attorney general, Secretary of State (Hillary) Clinton and many others.
"Mr Megrahi has been sent back to Libya to die a convicted man."
MacAskill would respond to Mueller's letter in due course, the spokesman added.
The semi-autonomous Scottish government, based in Edinburgh, can take decisions independently of London on justice matters but not foreign affairs.
Meanwhile, the British government came under pressure to explain its role in al-Megrahi's release, but strongly denied Libyan claims it was linked to trade deals.
As Megrahi was shown meeting Muammar Gadddafi, the Libyan leader, on television following his return home to Tripoli, Gaddafi's son Saif al-Islam said his release had often been raised in talks with Britain over oil and gas.
Islam told Libyan television: "In all commercial contracts, for oil and gas with Britain, (al-Megrahi) was always on the negotiating table."
But Peter Mandelson, Britain's business secretary and Prime Minister Gordon Brown's de facto deputy, categorically denied that a deal had been struck with Libya to allow al-Megrahi to walk free.
Speculation about the role played by London was fuelled by the disclosure that Mandelson had met Islam twice this year and Mandelson admitted that Islam had raised the issue of al-Megrahi on each occasion.
"They had the same response from me as they would have had from any other member of the government -- the issue of the prisoner's release was entirely a matter for the Scottish justice minister," he said.
"There is absolutely no question whatsoever... of a brokered deal or no agreement between the Libyan government or the British government."
Mandelson said that to suggest any agreement had been struck over al-Megrahi, the only person convicted for the murders of 270 people in the bombing of an airliner over the Scottish town of Lockerbie in 1988, was "offensive".
But British opposition parties said Brown had serious questions to answer over the decision to free al-Megrahi and should make it clear whether he believed al-Megrahi's release was right.