Claims that police tried to smear murder victim Stephen Lawrence's family will be investigated by two existing inquiries, Theresa May has said.
The home secretary also told MPs there should be a "ruthless" purging of corruption from police ranks.
It comes after undercover officer Peter Francis said he was instructed in 1993 to find information that could discredit the Lawrence family.
Stephen's father, Neville, said "only a judge-led public inquiry will suffice".
Scotland Yard has refused to confirm or deny the claims made in the Guardian newspaper by Mr Francis.
Black teenager Stephen, 18, was stabbed to death in an unprovoked attack by a gang of white youths as he waited at a bus stop in south-east London in April 1993.
A number of suspects were identified soon after the attack but it took more than 18 years to bring his killers to justice. An inquiry accused the police of institutional racism and found failings in how they had investigated the murder.
Working as part of the Met's now-disbanded Special Demonstration Squad, which specialised in gathering intelligence on political activists, he said he had come under pressure to find "any intelligence that could have smeared the campaign" - including whether any of the family were political activists, involved in demonstrations or drug dealers.
Mr Francis, who used the name Peter Black while under cover, said the aim of his operation had been to ensure that the public "did not have as much sympathy for the Stephen Lawrence campaign" and to persuade "the media to start maybe tarring the campaign".
Mrs May said the Lawrence family had "experienced an unspeakable tragedy".
She continued: "Their pain was compounded by the many years in which justice was not done, and these allegations still coming 20 years after Stephen's murder only add to their suffering."
Any investigations should be "ruthless in purging" corruption and wrongdoing from police ranks, she said.
Barrister Mark Ellison QC - who successfully prosecuted Gary Dobson and David Norris for Stephen's murder in 2012 - is already examining police corruption during the original investigation into the killing.
Mrs May told the Commons that he would look at the latest allegations as well.
And they would also be looked at as part of Operation Herne, which is an investigation into undercover policing at the Metropolitan Police, being led by the chief constable of Derbyshire police, Mick Creedon.
The Independent Police Complaints Commission (IPCC) is supervising some strands of Operation Herne.
Mrs May said: "Where the Creedon investigation finds evidence of criminal behaviour or misconduct by police officers, the IPCC will investigate and the officers will be brought to justice".
Neville Lawrence said the latest news had taken away the faith he had started to build in the police.
"It is unthinkable that in the extremely dark days and months after my son's murder that my family were subject to such scrutiny," he said in a statement.
"I understand that the home secretary has announced that she will extend the inquiries of Mark Ellison QC and Operation Herne, I would like to make it clear that I find this completely unsatisfactory.
"I have no confidence that the measures announced today will get to the bottom of this matter."
Prime Minister David Cameron said earlier he wanted to "get the full truth out" about the latest "horrific" allegations.
The IPCC said it was expecting to receive information from the Met in connection with the allegations "which may raise potential conduct matters" about officers from the Special Demonstration Squad.
Metropolitan Police commissioner Sir Bernard Hogan-Howe said: "If these allegations are true, it's a disgrace, and the Metropolitan Police Service will apologise."
He added: "Smearing the family of a murder victim would never be acceptable to me or my officers".
The Metropolitan Police said in a statement: "At some point it will fall upon this generation of police leaders to account for the activities of our predecessors, but for the moment we must focus on getting to the truth."
The man who was in charge of the Met between 1993 and 2000, former commissioner Lord Condon, said he had had no knowledge of any campaign to smear the Lawrence family.
"I can say categorically that at no time during my time as commissioner did I authorise or condone or was aware of the sort of smear operation that's been described in the Guardian," he said.
London Mayor Boris Johnson, whose responsibilities include oversight of the Met, said he had already spoken to current commissioner Sir Bernard about the claims and pledged to "leave absolutely no stone unturned".
Mr Lawrence's mother, Doreen Lawrence, said earlier that she was shocked and angry at Mr Francis's disclosure.
"Out of all the things I've found out over the years, this certainly has topped it," she said.
"It just makes me really, really angry that all of this has been going on and all the time trying to undermine us as a family."
Dispatches is broadcast on Channel 4 on Monday 24 June at 20:00 BST.