Gary McKinnon's legal team has welcomed Prime Minister David Cameron's suggestion that the computer hacker could spend any conviction imposed in a British jail.
And Mr McKinnon's lawyer Karen Todner insisted that the only "appropriate solution" was for her client to stand trial in Britain.
"We're very pleased that David Cameron has raised this and had a face-to-face discussion about Gary.
"Mr Obama has used the term 'appropriate solution' and the appropriate solution is that he stands trial in the UK," she said.
Mr McKinnon, who suffers from Aspergers syndrome, is accused of hacking into US government computer systems linked to national security.
But the Wood Green man insists that he was merely looking for evidence of UFOs.
Both Mr Cameron and Deputy Prime Minister Nick Clegg have publicly condemned plans to extradite Mr McKinnon to the US, where he could face up to 60 years in jail.
Speaking at a White House press conference alongside President Obama on Tuesday, the PM said: "We completely understand that Gary McKinnon stands accused of a very important and significant crime in terms of hacking into vital databases and nobody denies that is an important crime that has to be considered."
Mr Cameron said the government had been working with the US ambassador on options "where perhaps some of the sentence - if there is a prison sentence - is served in a British prison."
But he failed to reiterate his stance of last year when he said there was "a clear argument to be made that he should answer them in a British court."
Mr McKinnon's mother Janis Sharp said she was delighted her son's case had been raised by the Prime Minister.
She told GMTV: "It was amazing that we've now got someone brave enough in government to actually stand up and to raise it with Obama."
Speaking in the Commons, Mr Clegg said both Britain and the US were trying to "find a way forward.
"No one doubts the gravity of the offences which he is alleged to have committed - that is beyond question.
"The simple question is whether he should in these circumstances be tried here or extradited to the United States."
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