The former Commissioner, whose time at the head of the force was dominated by the case, said he was "shocked and dismayed" by allegations made by a former undercover officer.
Peter Francis, who reportedly posed as an anti-racist activist in the mid-1990s, said he came under "huge and constant pressure" to "hunt for disinformation" to undermine those arguing for a better investigation into the murder.
Scotland Yard says it is "not prepared to confirm or deny" the truth of the claims, which surfaced as a result of a joint investigation into undercover policing by the Guardian and Channel 4's Dispatches programme, to be broadcast tonight.
Downing Street said the prime minister believes Scotland Yard has "very serious questions" to answer and home secretary Theresa May will give further details of the demanded investigation in an emergency statement to the Commons later.
London Mayor Boris Johnson condemned as "utterly disgraceful" the activities described by Francis, who says he was told to dig up "dirt" shortly after the 18-year-old was killed in a racist attack in April 1993.
Francis said he was also asked to target the friend who witnessed the murder and campaigners angry at the failure to bring his killers to justice.
In a statement, Lord Condon said such actions - and the keeping of them from the Macpherson Inquiry into the case which found the Met guilty of institutional racism - would be "clearly wrong".
"I am shocked and dismayed by the allegations made by the former undercover police officer Peter Francis," he said.
"I am aware how distressing these allegations must be for Mr and Mrs Lawrence, and I am anxious they should know the truth as soon as possible.
"Throughout the time I was Commissioner I was never aware of, nor did I authorise or condone any police officers being tasked to smear Mr and Mrs Lawrence in the way suggested by Peter Francis.
"Nor was I ever aware of the deliberate withholding of relevant information from the judicial inquiry headed by Lord Justice Macpherson. Any such actions would have been clearly wrong.
"I am aware in recent decades that brave undercover officers have helped prevent terrorism, disrupt organised crime and reduce the likelihood of life-threatening serious public order in London. In my time as Commissioner, I was able to meet and thank some of these officers.
"I am anxious that the truth of these allegations should be established as soon as possible and I will do all in my power to help that process.
"I hope any review will also establish a clearer legislative framework for the legal, ethical and moral challenges faced by undercover officers and their senior officers."
Jack Straw, who as home secretary commissioned the Macpherson report, is to refer the case to the Independent Police Complaints Commission.
Lawrence, an aspiring architect, was stabbed to death by a group of up to six white youths in an unprovoked racist attack as he waited at a bus stop in Eltham, south east London.
In January 2012 Gary Dobson and David Norris were found guilty of being involved in the attack and sentenced to life imprisonment, after a forensic review of the case found significant new scientific evidence on clothing seized from their homes following the murder.
Lawrence's mother, Doreen, told the Guardian: "Out of all the things I've found out over the years, this certainly has topped it."
She added: "Nothing can justify the whole thing about trying to discredit the family and people around us."
The prime minster's official spokesman said May would set out "how best we believe the recent allegations should be responded to" to ensure it had the confidence of both the family and the public.
"It is very important there is a process that can command the confidence of Stephen Lawrence's family and the public," he said.
"There are very urgent questions that need answering."
Johnson revealed that had "lengthy" discussions with present Commissioner Sir Bernard Hogan-Howe about the allegations on Friday.
"I think it is utterly disgraceful that the Metropolitan Police Service were engaged in this kind of activity whether it is surveillance or trying to discredit the campaign to vindicate the memory of Stephen Lawrence," he said.
"It is very important that the family of Stephen Lawrence get answers to what I think is an absolutely deplorable series of allegations as soon as possible."
A Met Police spokesman said: "The claims in relation to Stephen Lawrence's family will bring particular upset to them and we share their concerns."
He added: "The Met must balance the genuine public interest in these matters with its duty to protect officers and former officers who have been deployed undercover, often in difficult and dangerous circumstances.
"We are therefore not prepared to confirm nor deny the identity of individuals alleged in the media to have been working undercover, nor confirm nor deny the deployment of individuals on specific operations."