Anwar, who is one of the most potent threat to Prime Minister Najib Razak, began a five-year jail term on February 10 after Malaysia's top court ruled there was overwhelming evidence that the 67-year-old leader sodomised the aide.
Anwar's daughter, Nurul Nuha, said the family had submitted an appeal for a royal pardon in the belief that Anwar is innocent.
"By virtue of Article 42 of the Federal Constitution, we hope that the Royal institution would in the name of justice based on all the facts grant an appeal," Nuha said.
Opposition PKR party's communications director Fahmi Fadzil told The Star Online that despite the seeking of a pardon, the application for a review of the Federal Court's decision would go ahead as planned.
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PKR leaders had initially denied that Anwar's family would seek a royal pardon as it would be tantamount to an admission of guilt.
However, the latest move is seen as a desperate attempt to prevent Anwar from disqualification as a member of parliament at the end of the 14-day period to file a petition for pardon following the Federal Court's verdict.
The case was widely viewed as politically motivated to eliminate threats to the the now 58-year-old ruling regime.
It is the second disputed sodomy conviction for Anwar, who has been the most vocal and visible symbol of the opposition's resurgence.
He was earlier arrested and jailed for six years on previous sodomy and corruption charges in a bitter power struggle in 1988.
In Muslim-majority Malaysia, homosexuality is a crime punishable by up to 20 years in prison and by whipping, although prosecutions are rare.