The Foreign Office said it has had engaged in talks with Washington's representative to London after the wife of a US official fled the UK following her suspected involvement in a fatal crash on August 27.
The British Government has been urging officials in the US to facilitate the return of the suspect, Anne Sacoolas.
The collision between a Volvo and a motorbike saw 19-year-old Mr Dunn lose his life.
In a statement issued on Tuesday evening, Whitehall said: "The Foreign Secretary met the US Ambassador today and urged the US to reconsider its position and do the right thing by Harry Dunn’s family."
It is unclear what the outcome of the talks is and if the US will be compelled to see the diplomat's wife returned to Britain.
Tuesday's call comes after Mr Raab engaged in talks with Mike Pompeo, the US President's right hand man, earlier in the week.
Harry Dunn, who was killed in the crash near RAF Croughton in Northamptonshire, was said to be a "big-hearted" and "fun-loving" son by his family
Urging Mrs Sacoolas to return to the UK, his family said: "We need her to face the consequences," before adding they are willing to cross the Atlantic to see her face "justice".
Diplomatic Immunity can be claimed by officials of foreign governments to allow them to avoid prosecution in their home nations.
In certain circumstances it can also apply to the spouses and partners of those posted to foreign nations.