Mr Khurts, 41, is wanted for kidnapping a Mongolian national suspected of murdering a government official.
His appeal was rejected by the High Court on Friday.
Lord Justice Moses and Mr Justice Foskett dismissed his appeal but his lawyers said the case may now be taken to the European Court of Human Rights.
Mr Khurts was allegedly involved in the 2003 kidnap of Enkhbat Damiran, who was taken from France to Berlin, drugged and flown to the Mongolian capital, Ulan Bator.
Mr Damiran was wanted in connection with the murder of Mongolia's Infrastructure Minister Zorig Sanjasuuren in 1998.
'Lured to UK' At the hearing earlier this year his lawyer, Alun Jones QC, claimed Mr Khurts, head of the executive office of Mongolia's National Security Council, should not have been detained at Heathrow Airport in September because he was covered by diplomatic immunity.
Mr Jones said Mr Khurts was lured to the UK by the Foreign Office, on the pretence of attending high-level government talks on intelligence co-operation, so he could be arrested and extradited to Germany.
Mr Jones said Mr Khurts had been granted a business visa for a visit during which he was supposed to meet Britain's National Security Adviser, Sir Peter Ricketts, and strategy and counter-terrorism director, William Nye.
Judge Purdy said he believed Mr Khurts was invited for genuine security talks but the Serious Organised Crime Agency (Soca) had heard about it and were aware of the outstanding warrant from Germany.