Ahmed had dual British-Pakistani citizenship before being stripped of his UK passport following his 2012 conviction for multiple counts of rape and sexual offences against girls.
He was one of nine men from Rochdale and Oldham found guilty of exploiting girls as young as 13 at two takeaway restaurants.
Andrabi said Ahmed’s “heinous crimes demand serious introspection rather than the quest to search for extraneous causes”.
He said: “The matter in question is entirely an internal matter of the United Kingdom.
“The individual concerned is a British national who spent his entire adult life in the UK and was duly convicted by a British court for reprehensible offences committed on British soil.
“Any decision regarding his release, supervision of usual legal status, falls exclusively within the jurisdiction of the competent British authorities and must be dealt with in accordance with the laws of the United Kingdom.
“Regardless of where he was born, the onus lies on where he grew up, was raised, groomed, and unfortunately spoiled.”
He added: “The government of Pakistan has no connection whatsoever with this matter.
“We cannot be associated with any decisions relating to the individual’s release or subsequent treatment under the British law.”
Ahmed was jailed for 22 years and released on licence this month.
Victims of the gang were told provisions under the Immigration Act 1971 barred the removal of any Commonwealth citizen who arrived in the UK before 1973 and had been in the country for five years.
Under the UK government’s proposed amendment, foreign criminals would no longer benefit from these protections where they are guilty of some serious crimes.
It would bring the law on deportation in line with the law on the removal of citizenship.
Home Secretary Shabana Mahmood this week said the 1971 Act provided protections for long-term UK residents but “should not be used as a bar against removal in cases like that of Shabir Ahmed”.
The Home Office has acknowledged that Ahmed’s removal depends on Pakistan accepting him.
Conservative shadow home secretary Chris Philp said the government should consider using “very robust measures to essentially compel” Pakistan to accept the return of Ahmed.
Speaking to Radio 4’s World At One programme, Philp said ministers had a couple of options: to suspend bilateral overseas aid payments completely, and “the most extreme level”, to apply visa sanctions to prevent Pakistani nationals entering the UK.
Philp said: “If a British citizen commits a crime somewhere else, we would accept them back and I would expect other countries to do the same when the boot’s on the other foot.”
Government data released on Thursday showed £51m of aid money would be given to Pakistan in each of the next three years.
Downing Street said the payments would not feature in the negotiations over Ahmed because the money did not go directly to the Pakistani government.
After leaving prison, Ahmed was sent to 24-hour staffed accommodation and fitted with a GPS electronically monitored tag.
While he is in the UK, the government has said he would be returned to prison if he breaches a series of strict licence conditions.
Some of his victims said they were “frightened” and felt “unsafe” at his release.
Andy Burnham, who is set replace Sir Keir Starmer as prime minister next, has described Ahmed as a “vile criminal” whom he wants deported.
