Mr Mohamed, a British resident, claims he was tortured in US custody
Police are to investigate whether an MI5 officer was complicit in the torture of ex-Guantanamo detainee Binyam Mohamed.
The Attorney General, Baroness Scotland QC, said the probe would be "the appropriate course of action".
Mr Mohamed, 30, a UK resident, said MI5 had prolonged his detention and torture while he was being held in Morocco.
The MI5 agent who questioned him has denied threatening or putting any pressure on Mr Mohamed.
'Seriousness and sensitivity'
Ethiopian-born Mr Mohamed says he was tortured while in US custody in Pakistan, Morocco and Afghanistan, with the complicity of MI5.
He says that in Morocco in 2002, he was mistreated by local officers who asked him questions supplied by British intelligence.
Frank Gardner, BBC security correspondent
This is the first time in living memory that anyone can remember the police being asked to investigate MI5, the Security Service.
As the two organisations working side-by-side on the front line of Britain's fight against terrorism it is an extraordinary and for some, uncomfortable situation.
The official Home Office position is that MI5 will co-operate fully with any police investigation.
Initially this is likely to focus on the MI5 officer known in court documents as 'Witness B'.
This is the man sent out to Pakistan to question Binyam Mohammed in 2002, at a time when he was suspected of being part of a major al-Qaeda plot.
But any police probe is unlikely to stop there. That MI5 officer sent back reports to London, so how much did his superiors know about Mr Mohamed's treatment and did they authorise co-operation with the CIA and his interrogators to continue, regardless?
Awkwardly for the Security Service, the man running International Counter-Terrorism at MI5 at the time was one, Jonathan Evans.
He's now the Director General, yet he may soon find himself helping police with their enquiries.
Mr Mohamed returned to the UK in February 2009 after seven years in custody - four of which were spent in the US camp at Guantanamo Bay.
BBC security correspondent Frank Gardner said the investigation would focus on an MI5 officer known as Witness B, who travelled to Karachi in 2002 to question Mr Mohamed.
It is alleged that Witness B told Mr Mohamed that his only way out of Pakistani custody was to co-operate fully, and that the officer knew to where Mr Mohamed would be subsequently rendered.
Baroness Scotland said she had invited the Metropolitan Police Commissioner, Sir Paul Stephenson, to begin an inquiry.
"I have expressed to the commissioner the hope that the investigation can be taken forward as expeditiously as possible given the seriousness and sensitivity of the issues involved," she said.
"The conduct of the investigation will be a matter for the police, with advice from the Crown Prosecution Service."
The allegations were referred to law officers in 2008 by Home Secretary Jacqui Smith.
In a statement, she said the government and the security services would co-operate fully with the police if asked.
"Wherever allegations of wrongdoing are made, they are taken seriously," Ms Smith added.
Prime Minister Gordon Brown insisted that the UK did not tolerate torture, but said the security services had his unequivocal support.
"I want to stand up for our security services because they cannot stand up for themselves," Mr Brown added.
But Zachary Katznelson, the legal director of charity Reprieve, whose lawyers represent Mr Mohamed, said he was concerned that crucial evidence would be kept from the inquiry.
"Many of the documents related to Mr Mohamed's treatment have been classified either in the US or the UK and unless the police have access to all of them, they will only see one tiny piece of the picture," he added.
Shadow justice secretary Dominic Grieve said Mr Mohamed's claims raised broader concerns.
"It goes to the entire issue of the involvement of the British security services with the activities of others who may have committed torture not just on him but on other people as well," Mr Grieve added.
Former shadow home secretary David Davis said there was "a very serious case to answer".
He added: "It is vital that this investigation does not simply select a low-ranking MI5 officer as a scapegoat, but establishes where the responsibility for approving these actions originated, no matter how high they go."
Liberal Democrat foreign affairs spokesman Edward Davey welcomed the announcement.
But he warned that the "wider question of the government's policy on rendition and torture throughout the Bush and Blair years will remain unanswered" until a full judicial inquiry was held.
Amnesty International UK's head of policy and government affairs Jeremy Croft said the decision was just a "first step".
"We still need an independent inquiry with the powers to unearth any wrongdoing by UK officials during the 'war on terror'," he added.
Moazzam Begg, a British former Guantanamo Bay inmate, said he had spent several days with Mr Mohamed since the end of his "terrible ordeal".
Mr Begg added: "It's fantastic news.
"We've been saying this for so many years now - that the MI5 were present at every leg of my journey during my extraordinary rendition, that included in Afghanistan, in Pakistan and Guantanamo Bay."
Scotland Yard confirmed it had been asked to begin an investigation.
A spokesman added: "A decision on how this will be taken forward will be made in due course."
Mr Mohamed arrived in the UK in 1994 and sought asylum on the basis of his family's opposition to the Ethiopian government.
His application was rejected, but in 2000 he was given exceptional leave to remain in the UK for four years.