An influential government committee has urged home secretary Alan Johnson to use his discretion in evaluating the case of Nasa hacker Gary McKinnon.

Keith Vaz, the chair of the the Home Affairs Select Committee, sent a letter to Johnson on Thursday asking him to halt the extradition of McKinnnon to the US to face hacking charges.

McKinnon, who has Asperger's syndrome, is in a parlous mental condition, Vaz wrote in a letter seen by ZDNet UK.

"Because of Mr McKinnon's precarious state of mental health, the Committee is of the view that he should not be extradited to the USA and that you should exercise your discretion in this case," wrote Vaz.

In a hearing on Tuesday the committee questioned Johnson about his views on the McKinnon case and on the extradition treaty that the UK has with the US.

Johnson told the committee on Tuesday that he was "carefully considering" psychiatric evidence submitted to him by McKinnon's defence team, which said that McKinnon was at risk of suicide if extradited, to judge whether extradition would infringe McKinnon's human rights.

Johnson added that in his view the extradition treaty was balanced, as the burden of proof required to secure an extradition was approximately equal on both sides.

On Thursday the Home Affairs Select Committee disagreed with Johnson, saying that the treaty was not balanced.

"The Committee remains concerned that there is a serious lack of equality in the way the treaty's provisions apply to UK, as opposed to [US], citizens," wrote Vaz.

Vaz went on to recommend that the operations of the treaty be "reviewed comprehensively", and said that in the case of McKinnon, Johnson had more scope to act than he had stated.

The Home Office on Thursday insisted that the treaty was balanced.

"As the home secretary told the Home Affairs Select Committee on Tuesday, the evidence that must be provided for a US extradition request to proceed in the UK is in practice the same as for a UK request to proceed in the US," a Home Office spokesperson said in an email statement.

The spokesperson added that Johnson's discretion was only within the scope of whether extradition would amount to a breach of McKinnon's human rights.

The Liberal Democrats on Thursday called for Johnson to halt McKinnon's extradition.

"It is not in the interests of justice to send a British citizen with mental health problems to face decades in an American jail," said Liberal Democrat shadow home secretary Chris Huhne in a statement. "The home secretary must put an end to this shameful episode and then renegotiate the extradition treaty so this fiasco is not repeated."

McKinnon is accused by the US of "the biggest military hack of all time". US prosecutors allege that McKinnon accessed 97 military computers between 2001 and 2002, causing $700,000 (£400,000) damage. McKinnon admits hacking the systems but denies the damage. He has consistently claimed to have been searching for evidence of extraterrestrial life.