Australian citizen Dr Gerald Toben was remanded in custody after his arrest by British Police at Heathrow Airport.
German authorities allege Dr Toben published material online "of an anti-semitic and/or revisionist nature".
But home affairs spokesman Chris Huhne said holocaust denial is not a crime in the UK and he should not be extradited.
Dr Toben, a German-born former schoolteacher, was en route from the United States to Dubai when he was arrested.
He has been remanded in custody ahead of a bail hearing on 10 October and a full hearing on 17 October.
He has previously been convicted in Germany for breaking a law that prohibits denying or "playing down" the mass murder of the Jews under Hitler.
We don't in this country tend to prosecute people for issues that we regard as issues of freedom of speech
But some human rights campaigners have backed his case, saying that his views - however unpleasant - do not make him a criminal in the UK.
The Crown Prosecution Service (CPS), acting for the German authorities, argues that agreements signed in 2003 between the UK and other European countries mean that Britain is duty-bound to assist the German authorities.
But Mr Huhne, a former MEP, told BBC Radio 4's Today Programme that countries could "pick and choose" cases in which they would apply warrants issued by fellow EU member states.
The Lib Dem home affairs spokesman said there were good legal grounds for refusing to participate. He cited the case of Belgium, which is refusing to send suspects to Poland on murder charges which related to abortion.
Mr Huhne said: "There is a clear precedent for doing this and I think we should in this case."
Dr Toben has in the past described the Holocaust as "a lie" and has claimed on his Australian-based website, the Adelaide Institute, there was "no proof" Hitler systematically exterminated the Jews.
While stressing that he was completely opposed to anti-semitism, Mr Huhne said: "We don't in this country tend to prosecute people for issues that we regard as issues of freedom of speech."
Mr Huhne said the case seemed "pretty dodgy" given the fact the offence was not committed in Germany.
In his court appearance earlier this week, Dr Toben, 64, claimed he was the victim of a "legal ambush" and promised never to return to Britain if he was allowed to leave.
Judges will decide whether the alleged conduct constitutes an extraditable offence.
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