Many relatives of the 270 people killed in the bombing of a Pan Am airliner over the Scottish town of Lockerbie are still outraged over al-Megrahi's release.
The vast majority of the passengers were from the United States.
John Brennan, counter-terrorism adviser to the US president, said on Friday that the release was "unfortunate, inappropriate and wrong".
A spokeswoman for the UK foreign office said al-Megrahi "was convicted for the worst act of terrorism in British history".
"On this anniversary we understand the continuing anguish that al-Megrahi's release has caused his victims, both in the UK and the US," the spokeswoman said.
Speaking to Reuters, one senior Libyan source was quoted as saying: "This year, Libya's leadership is keeping quiet while they secretly enjoy their success."
"They do not need to trumped it anew."
Scotland took the decision to release the bomber on compassionate grounds on August 20 last year, saying he was seriously ill with prostate cancer and had only a couple of months to live.
Abdelhakim Ali said Libyan authorities told the family not to comment on "the condition of his health" on the anniversary.
Al Jazeera's Alan Fisher, reporting from Edinburgh, the Scottish capital, said: "Many people are surprised that he [al-Megrahi] is still alive one year on.
"There's no doubt that the release of the Lockerbie bomber ... is still a big political argument."
"Libya needs BP and BP needs Libya"
Oliver Miles, former British ambassador to Libya
He said the Americans are calling the release not "[a] compassionate ... but [a] convenient release [as] so many people benefited from the decision to free al-Megrahi".
"There're some who say that the whole Scottish legal system benefited because there were questions over the conviction.
"If al-Megrahi had gone to a second appeal then that conviction would have been challenged perhaps overturned and the question would have been left: Who is actually behind the Lockerbie bombing?"
Al-Megrahi was released after serving eight years of a minimum 20-year sentence.
"There are people in Scotland who request compassionate release and don't get it," Susan Cohen, whose 20-year-old daughter, Theodora, died in the bombing, said.
"There are people who die in Scottish prison," the 72-year-old US resident told The Associated Press news agency, adding "[al-Megrahi] may outlive me".
Alex Salmond, Scotland's first minister, said al-Megrahi's release "had been done following the precepts of Scottish jurisdiction and Scots law".
"Some people say that the Scottish system has too much compassion," he said.
"But at the end of the day, I think I'd rather be first minister of a society with too much compassion than be first minister of a country with too little compassion."
Some groups have speculated that energy company BP pressured the government to release al-Megrahi.
US senators allege the firm played a part in securing the bomber's release as part of its efforts to seal a lucrative exploration deal with Tripoli.
The US senate's foreign relations committee wants to hold a hearing into the affair in the coming weeks.
Officials in Britain deny BP was involved in the affair and the Scottish government has declined to send ministers to Washington to appear before the hearing.
A former British ambassador to Libya told Al Jazeera that there was "nothing fishy at all about" linking BPs oil deals to al-Megrahi.
"When Tony Blair [the former British prime minister] went to Libya, he was responsible for negotiating several issues [including policies affecting prisoners and the BP deal]," Oliver Miles said.
Miles said the BP deal would have happened, regardless of al-Megrahi's release.
"Libya needs BP and BP needs Libya," he said.