Tony Blair says he was not made aware of the abduction of Libyan dissident Abdul Hakim Belhaj until after he had left office in 2007.
Prime Minister Theresa May has apologised to Mr Belhaj, who in 2004 was seized by the CIA and sent to Libya with the assistance of MI6.
Mr Belhaj says he was tortured by Col Muammar Gaddafi's forces.
Mr Blair - who was prime minister at the time - said he was "content to go along" with Mrs May's apology.
Mrs May said Mr Belhaj and his wife, Fatima Boudchar, had suffered "appalling treatment", in a letter of apology earlier this month.
Ms Boudchar, who was pregnant at the time, has accepted Mrs May's apology and will receive a £500,000 payout.
The couple say an MI6 tip-off helped the US kidnap them in Thailand.
Mr Belhaj was taken to Tripoli and says he was tortured by his Libyan jailers during a six-year spell in prison. Ms Boudchar was also detained but was released shortly before giving birth.
Mr Blair told BBC Radio 4's Today programme: "I have gone along with what the government has done, which is to issue an apology.
"I didn't actually know about this case myself until I left office.
"So, I'm content to go along with that apology."
He added: "I am sorry for any mistreatment that's been given to people.
"I have always been wholly and 100%, in all circumstances, opposed to the use of torture."