A Libyan military commander is taking legal action against Jack Straw, to find out if the ex-foreign secretary signed papers allowing his rendition.
Abdel Hakim Belhadj claims CIA agents took him from Thailand to Gaddafi-led Libya, via UK-controlled Diego Garcia.
His lawyers have served papers on Mr Straw after the Sunday Times reported claims that he allowed this to happen.
UK ministers have denied any complicity in rendition or torture and Mr Straw did not comment further.
He said he could not do so because of the ongoing police investigation into the UK's alleged role in illegal rendition.
Earlier this month, the BBC revealed that the UK government had approved the rendition of Mr Belhadj and his wife - Fatima Bouchar - to Col Muammar Gaddafi's regime, though it was unclear at what level.
On 15 April, the Sunday Times published an article, which quoted sources as alleging Mr Straw had personally authorised Mr Belhadj's rendition to Libya.
On Tuesday, Mr Belhadj's lawyers - Leigh Day & Co - served papers on Mr Straw, referencing the article and seeking his response to allegations that he was complicit in torture and misfeasance in public office.
The civil action is against Mr Straw personally - Mr Belhadj's lawyers believe it is the first time legal action of this kind has been taken against a former foreign secretary.
Mr Belhadj and his wife allege Mr Straw was complicit in the "torture, inhuman and degrading treatment, batteries and assaults" they say were perpetrated on them by Thai and US agents, as well as Libyan authorities.
They are seeking damages from Mr Straw for the trauma involved.
'Inhuman and degrading treatment'
In 2004, Mr Belhadj was the leader of the Libyan Islamic Fighting Group (LIFG) and was living in exile after leading opposition to the Gaddafi regime. MI5 had believed LIFG was close to al-Qaeda.
Mr Belhadj alleges he and his wife were detained by CIA agents in Bangkok as they travelled to Britain to claim political asylum - he believes the plane they were transported on refuelled at the UK territory of Diego Garcia, in the Indian Ocean.
Mr Belhadj claims that he and his wife were tortured during the rendition process and in Libya, where he was subsequently imprisoned.
Papers have already been served in the High Court to sue the UK government, its security forces, and senior MI6 officer Sir Mark Allen, for damages.
Mr Belhadj's lawyers said their letter of claim against Jack Straw relied on the same allegations and evidence set out in the letters to Sir Mark and the government.
They said Mr Straw had been foreign secretary with responsibility for MI6 at the time of Mr Belhadj's rendition and that a 2004 letter from Sir Mark to Libya's former intelligence chief congratulated the Libyans on Mr Belhadj's safe arrival.
'Neither confirm nor deny'
The lawyers said they anticipated Mr Straw's response would mirror the government solicitor's "neither confirm nor deny" response to their previous letters of claim regarding Mr Belhadj.
They said therefore that, while Mr Straw would ordinarily have six months in which to respond their allegations, they sought a response by close of business on 17 May "following which proceedings may be issued against you without further notice".
If Mr Straw did not admit liability within that time, they said they expected him to provide copies of the documents described in the Sunday Times article and copies of government communication and memos relating to Mr Belhadj.
Sapna Malik, a partner at law firm Leigh Day & Co representing Mr Belhadj and his family, said she believed Mr Straw did approve Mr Belhadj's rendition.
"If the former foreign secretary does not now own up to his role in this extraordinary affair, he will need to face the prospect of trying to defend his position in court."
The Metropolitan Police are investigating Mr Belhadj's claims and Ms Malik said if their inquiry was broadened, Mr Straw could face criminal prosecution.
In an interview with BBC Radio 4 last year, Mr Straw said the Labour government had been opposed to unlawful rendition.
"We were opposed to any use of torture or similar methods. Not only did we not agree with it, we were not complicit in it and nor did we turn a blind eye to it."
But Mr Straw added, "No foreign secretary can know all the details of what its intelligence agencies are doing at any one time."