Lord Ahmed, 55, was freed by the Court of Appeal after serving 16 days of his 12-week prison sentence in 2009 for dangerous driving.
The Pakistan-born property developer later supported an AA/Populus poll into mobile phone use among motorists, saying he had "learnt the hard way" about the problem.
The peer was suspended from the Labour Party for three months last year over reports he offered a $10 million (£6.7 million) "bounty" for the capture of Barack Obama and George Bush.
Lord Ahmed denied having made the comments, published in a Pakistani newspaper, and was reinstated after an investigation by Labour Lords Chief Whip Lord Bassam.
Lord Ahmed was sentenced in 2009 after pleading guilty to dangerous driving, having sent and received text messages in the build up to a fatal crash on the M1 near Sheffield on Christmas Day in 2007.
The final message was sent two minutes before his Jaguar struck the stationary car of 28-year-old Slovakian Martyn Gombar.
No causal link was made between the text messages and Mr Gombar's death, though.
The Times said it gained four separate Urdu-English translations to verify Lord Ahmed's comments during a television interview, which it said were thought to have been made in April last year during his visit to Pakistan. The newspaper claims the peer is seen saying:
I was charged with a traffic offence, for texting while driving. A traffic offence, dangerous driving, and it should have gone to the magistrates court.
My case became more critical because I went to Gaza to support Palestinians. My Jewish friends who own newspapers and TV channels opposed this.
Labour's shadow chief secretary to the Treasury, Rachel Reeves has reacted to Britain's credit rating downgrade by the ratings agency Moody's:
UK credit rating downgraded by Moody's bcs of 'continuing weakness in the UK's medium-term growth outlook'. Time 4 a plan for jobs & growth.
Labour Leader - and Doncaster North MP - Ed Miliband made his big speech yesterday at the Labour Party Conference in Manchester. To the faithful was, naturally, warmly received, with one union leader saying it was the best he'd ever heard from him.
Our political correspondent, Ben Erlam, has been speaking to some of our region's MPs to see what they thought of their leader's speech.
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The Morley MP will pledge to hold a "zero-based spending review" to look at "every pound spent".Read the full story ›
Morley MP Ed Balls was on the score sheet as team of Labour politicians defeated a side of journalists in their annual grudge match.Read the full story ›
A Bridlington mum has been awarded compensation after suffering burns while undergoing an emergency caesarean section.Read the full story ›
Labour leader and Yorkshire MP Ed Miliband pledged today to work with unions to help the party rebuild the economy if it wins power again.Read the full story ›
Labour have today called for the Government to reverse its decision to slash funding for flood defences following devastating downpours across West Yorkshire. The shadow environment secretary Mary Creagh claimed cutting flood defence spending by a third could leave more homes at risk.
She said: "Communities that have been devastated by flooding should not have to go through that experience again." But Environment Secretary Caroline Spelman insisted prevention was "a vital area of the work of Government" and said ministers were spending £2 billion on measures to stop floods.
In some places a month's rain fell in 24 hours, leaving hundreds of homes swimming in dirty water and prompting forecasters to say the country could be on course for one of the wettest Junes of the last 100 years.