Barack Obama said he would "respect" the legal process in the case of British computer hacker Gary McKinnon who is wanted in the US, signalling his government was prepared to soften its stance.

There were calls for the US president to use his state visit to Britain to scrap American attempts to extradite the Asperger's sufferer.

The 45-year-old faces 60 years behind bars for hacking into Pentagon and Nasa computers between February 2001 and March 2002 while searching for evidence of "little green men".

There has been a long-running campaign for Mr McKinnon to be allowed to remain in the UK following warnings from medical experts that he could kill himself if sent to the US to face trial.

The case is currently before Home Secretary Theresa May, who has to make a final decision as to whether Mr McKinnon should be extradited.

Speaking during a press conference at Lancaster House, Mr Obama stopped short of abandoning US attempts to extradite Mr McKinnon.

But he seemed to offer the London-based computer hacker and his family a way out by saying he would respect the British legal process.

He said: "We have proceeded through all the processes required under our extradition agreements. It's now in the hands of the British legal system.

"We have confidence in the British legal system coming to a just conclusion, and so we will await resolution and we will be respectful of that process."

The Prime Minister, referring to Mr McKinnon by his first name, said he understood the "widespread concern" about the way he would be treated if handed over to the US authorities.

He said: "The case is in front of the Home Secretary who has to consider reports about Gary's health and his well-being and it is right that she does that in a proper and effectively quasi-judicial way.

"I totally understand the anguish of his mother and family about this issue. We must follow the proper processes and make sure this case is dealt with in the proper way and I am sure that is the case."

Earlier this week, there were calls for the coalition leadership to raise the issue with Mr Obama during his state visit.

McKinnon's case was raised with Deputy Prime Minister Nick Clegg on Tuesday by the hacker's constituency MP David Burrowes.

Speaking at Commons questions, Mr Burrowes (Enfield Southgate) said: "When the Prime Minister visited America, President Obama said (that) because of the unsurpassed special relationship between our countries an appropriate solution would be found.

"Can he assure me the case of Gary McKinnon is raised during the visit of the president and also that the 'appropriate solution' is to stop the extradition to the US?"

Mr Clegg said the Home Secretary would be reviewing new information "against the impact on his human rights".

Shami Chakrabarti, director of Liberty, said: "If, as the president says, he will be 'respectful' of our legal process, then he should be happy for Gary to be dealt with here in the UK.

"If our Government seeks to honour the words of both coalition partners in opposition, it will decide that Gary's condition warrants halting this farcical extradition immediately, so that justice and compassion can be dispensed at home."

Karen Todner, senior partner at Kaim Todner solicitors, said she was "absolutely delighted" if the US was relaxing its position.

She said Mr McKinnon's mother Janis Sharp described the President's comments as "very positive".

Ms Todner said: "Bearing in mind we do have this special relationship, the fact Mr Obama has come out and said he would respect the English judicial system is wonderful.

"It's affected every minute of every day of Gary's life for the last nine years. Most people are now aware of what Asperger's is. Even five years ago they were not so aware, but I think they (the US authorities) have at some point been consulted about that and they have seen the files which show how this whole process has detrimentally affected Gary's life."

It is not yet known when Mrs May will decide whether Mr McKinnon must be extradited.

A Home Office spokeswoman said: "Extradition can only be refused at this late stage in the process if the Home Secretary decides that extradition would breach Gary McKinnon's human rights.