Once there, British intelligence suggested to the Pakistani authorities he should be arrested.
A list of questions to be put to Ahmed was drawn up by the security services and Manchester police, said Mr Davis.
Ahmed has said he was whipped with tyre rubber, beaten with staves and had three fingernails pulled out.
Mr Davis accused the government of misusing arguments of national security to cover up complicity in torture.
He raised the case of Binyam Mohamed, a former UK resident who alleges he was tortured by US agents in Pakistan, Morocco and Afghanistan and that UK agencies were complicit in the practice.
In February, two British judges claimed they had been prevented from publishing details of Mr Mohamed's treatment by the government because the US had threatened to stop sharing intelligence with the UK if they did.
David Davis: "Our handling of the subject of torture has been completely wrong"
"The government has fought tooth and nail and used the law ruthlessly to prevent things coming out in the public domain," Mr Davis said.
"The two judges, very senior judges, one a law lord, dealing with the Binyam Mohamed case have been stopped from putting a summary, a very vetted summary, of the complicity of the US and UK governments in torture into the public domain.
"If you are using secrecy to either prevent political embarrassment or to cover up a crime, rather than protecting national security, then that secrecy is being misused."
Foreign Secretary David Miliband has said the US did not threaten to withdraw co-operation over the case and the government was opposed to the use of torture.
Mr Davis said he had used parliamentary privilege to make his claims because he was afraid of "tripping over the Official Secrets Act".
"Nothing that was said was not in the public interest to be in the public domain, but I also wanted to make very sure that I didn't suddenly find someone being prosecuted for doing something that was actually the right thing," he added.
The former shadow home secretary is now calling for a judicial inquiry into at least 15 cases where torture of terrorist suspects has been alleged.
Replying to Mr Davis, Foreign Office minister Ivan Lewis said he could not comment in detail on Ahmed's case for legal reasons.
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