Mr McKinnon faces 60 years in jail if convicted in the US
Home Secretary Alan Johnson has said he will study new medical evidence before approving the extradition to the US of computer hacker Gary McKinnon.
He said he had "stopped the clock" on proceedings to give Mr McKinnon's lawyers time to appeal in Europe.
Earlier this month the 43-year-old, who has Asperger's syndrome, was denied an appeal at the UK Supreme Court.
Mr McKinnon is accused of breaking into the US's military computer system but says he was just seeking UFO evidence.
Mr Johnson said he would examine the new medical evidence "very carefully".
He also said he wanted to give Mr McKinnon's lawyers time to examine medical reports and make legal representations to the European Court of Human Rights in Strasbourg.
Mr McKinnon, of Wood Green, north London, faces 60 years in prison if convicted in the US.
"We have stopped the clock ticking on the representation to the European Court because new medical evidence has been provided," Mr Johnson said.
"There are two issues upon which Gary McKinnon's legal advisors have argued: the first is that the Director of Public Prosecutions should have tried him in this country."
Mr McKinnon's supporters have campaigned for him to be put on trial in the UK on charges of computer misuse.
Mr Johnson has also been pressured to delay proceedings further until an inquiry into the US-UK extradition treaty had been carried out by the Commons Home Affairs Select Committee.
Critics of the treaty say it does not treat US and British citizens equally.
Mr Johnson said the High Court had already dismissed applications for him to be tried in the UK, but added: "I have to ensure that his Article 3 human rights are being respected.
"It's that new medical evidence that I will be looking at very carefully".
Mr McKinnon's MP David Burrowes, who represents Enfield Southgate, has described the new medical evidence as "compelling".