Lord Ahmed has apologised "completely and unreservedly" for blaming Jewish-owned media organisations for his imprisonment for dangerous driving.
He told the Huffington Post UK he could not "believe" it when he saw the Times reports of what he had said in a Pakistani television interview.
He said his comments were "completely wrong", "unacceptable" and the product of a "twisted mind" - but took "full responsibility" for them.
The peer has been suspended by Labour.
Lord Ahmed told the Huffington Post that he was not anti-Semitic and said he did not have "any explanation or excuse" for his comments.
"I only believe in facts and to be honest I should have stuck with the facts rather than with conspiracy theories," he told The Huffington Post, later reiterating his apology to the Press Association.
When he saw the video on The Times website of the interview he says was given two or three years ago he said: "I was horrified... I could not believe that this was me."
Asked if he had a message for Labour leader Ed Miliband, Lord Ahmed said: "He's of the Jewish faith and I'm sorry that I embarrassed him or anyone else in the Labour Party.
"I'm particularly sorry to all my colleagues in the House of Lords and in the House of Commons because one thing many of them know is that I'm not anti-Semitic or a conspiracy theorist."
Lord Ahmed's comments came in a television interview, thought to have been broadcast in April last year, while he was on a visit to Pakistan.
He told an Urdu-language broadcast he should have been sentenced by a magistrate but pressure had been placed on the courts to charge him with a more serious offence because of his support for Palestinians.
"My case became more critical because I went to Gaza to support Palestinians. My Jewish friends who own newspapers and TV channels opposed this," the Times reports him as saying in the television interview.
He said the judge who had sentenced him had been appointed to the High Court after helping a "Jewish colleague" of Tony Blair during "an important case", the newspaper adds.
Lord Ahmed was jailed for 12 weeks in 2009 after sending and receiving text messages while driving.
He was freed by the Court of Appeal after serving 16 days of the sentence because of "exceptional" mitigation relating to his community work.
He had been involved in a fatal crash minutes after sending the messages on Christmas Day 2007.
He pleaded guilty to dangerous driving but did not face the more serious charge of causing death by dangerous driving because no causal link could be established between his texts and the crash.
But the case was transferred from Sheffield Magistrates Court to Sheffield Crown Court for sentencing because the district judge in the case felt his sentencing powers were not sufficient.
The 55-year-old Pakistan-born businessman and Labour Party activist was appointed to the House of Lords by Tony Blair in 1998. He was one of the first three Muslim peers,
He was suspended and investigated by the Labour Party in 2012 after allegations he had called for a £10m bounty for the capture of US Presidents Barack Obama and George W Bush. He was subsequently cleared and reinstated.