The parents of Harry Dunn have been told by the UK government their claims of abuse of power by Foreign Secretary Dominic Raab are "without foundation".
The 19-year-old died in hospital after a crash in Northamptonshire in August. US suspect Anne Sacoolas left the UK claiming diplomatic immunity.
The teenager's parents allege the granting of immunity by Mr Raab was "wrong in law".
The Foreign Office (FCO) has written to the family rejecting the allegations.
It told the BBC it had sent a letter - seen by the BBC - to Mr Dunn's parents, Charlotte Charles and Tim Dunn, but would not comment on its content. It expressed its "deepest sympathy" to the family.
In the letter, the FCO said it would "seek costs" for any judicial review brought and argues the family has not found "any reasonably arguable ground of legal challenge".
It said the allegation that the foreign secretary had "misused and/or abused his power" was "entirely without foundation".
Mr Dunn's motorbike crashed with a car owned by Mrs Sacoolas, the 42-year-old wife of US intelligence officer Jonathan Sacoolas, outside RAF Croughton, near Brackley, on 27 August.
Northamptonshire Police has handed a file to the Crown Prosecution Service after interviewing Mrs Sacoolas in the US.
Family spokesman Radd Seiger said: "The FCO relies on two private agreements between the USA and UK dated in 1995 and 2001 to assert that Anne Sacoolas did have diplomatic immunity."
He added the family had taken legal advice and its "position is clear that these arrangements have no basis in law".
He continued: "As if it were not enough for the family to have to endure the loss of Harry, the British government now appear[s] intent on putting them through a needless and protracted legal battle culminating in court. So be it. They will not rest until justice is done. But shame on the government."