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.
His daughter Nurul Nuha said the family has submitted a plea for a royal pardon in the belief that Anwar is innocent.
"He is the victim of a gross miscarriage of justice and it is our constitutional right to seek to right that wrong," Nuha said.
She said: "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."
"We also would pursue and exhaust all available recourse provided for a citizen in this country," she said in a statement.
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.
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.
He has been convicted of sodomising his aide in the opposition campaign office in 2008, Mohamad Saiful Bukhari Azlan, then 23.
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.

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