The former prime minister said he only became aware of the case of Abdel Hakim Belhaj after leaving office in 2007.
He apologised "for any mistreatment that's been given to people" but said he was not involved in the 2004 decision to send Mr Belhaj and his wife, Fatima Boudchar, to Libya. Mr Blair was prime minister at the time.
Mr Belhaj was tortured in a Gaddafi regime prison and sentenced to death. Ms Boudchar, who was pregnant at the time, was hooded, shackled and strapped to a stretcher for the duration of the flight to Libya.
Earlier this month, Theresa May apologised to the pair for the "appalling" treatment they endured.
Asked about the case, Mr Blair told BBC Radio 4's Today programme: "This has been subject to a long legal process. I have gone along with what the government has done, which is issue the apology.
"I didn't actually know myself about this case until after I left office, so I'm content to go along with that apology, and that's all that's frankly sensible for me to say."
He added: "This case wasn't brought to my attention. There's a lot of things in this case, some of which have been out in the media, some of which have not. There's been a settlement of the case; as I say I'm content to go along with the government's apology in relation to it.
"It's not something I dealt with myself when I was in government."
Asked if he would personally apologise to Mr Belhaj and Ms Boudchar, he said: "Of course I'm sorry for any mistreatment that's been given to people - how on earth would you ever justify that?
"Let me make one thing clear because sometimes people say I was sort of ambivalent on the use of torture: I have always been wholly and 100 per cent in all circumstances opposed to the use of torture and I made that clear privately, publicly in any conversation I've ever had within government."
Documents uncovered during the 2011 Libyan revolution revealed MI6 agents had been involved in capturing Ms Belhaj and Ms Boudchar in Thailand in 2004. They were also interrogated by British intelligence officials.
Writing to the pair earlier this month, Ms May said: “It is clear that you were both subjected to appalling treatment and that you suffered greatly, not least the affront to the dignity of Mrs Boudchar who was pregnant at the time.
“The United Kingdom government believes your accounts. Neither of you should have been treated in this way.”
The letter was read out in the House of Commons by the attorney general, Jeremy Wright.
Ms Boudchar will be paid £500,000 in compensation by the UK government. Mr Belhaj's lawyers said he "did not seek and has not been given any compensation".
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