A Number 10 spokesman said the prime minister told the US president of the need for Anne Sacoolas to return to the UK, after the US rejected an earlier extradition request.
The 19-year-old died after his motorbike was hit by a car outside RAF Croughton in Northamptonshire in August last year.
A Number 10 spokesman said: “The Prime Minister raised the tragic case of Harry Dunn, and the need to secure justice for Harry’s family.
“He reiterated the need for the individual involved to return to the UK.”
Mrs Sacoolas, 42, claimed diplomatic immunity following the crash and was able to return to her home country, sparking an international controversy.
She was charged with causing Harry’s death by dangerous driving by the Crown Prosecution Service in December.
Business Secretary Andrea Leadsom met Harry’s family on Friday, the day after she had informed them of US Secretary of State Mike Pompeo’s decision to refuse the request.
Ms Leadsom held talks with US ambassador Woody Johnson, the commander of RAF Croughton Colonel Bridget McNamara and the Chief Constable of Northamptonshire Police.
The family’s constituency MP, Mrs Leadsom said she had expressed her disappointment on their behalf during the discussion with the US ambassador.
She told reporters that the prime minister is “very much on the side of the family in their desire to see justice done”, adding: “All of us in Government are working to that end.”
A spokesman for the US State Department said the request was rejected because it would render the invocation of diplomatic immunity a practical nullity and set an extraordinarily troubling precedent.
Foreign Secretary Dominic Raab said the move “amounts to a denial of justice” as he expressed the Government’s disappointment at the decision.
The Foreign Office maintains the suspect had diplomatic immunity, which has been disputed by the family, but Mr Raab said he would look to “resolve the issue” surrounding any immunity given to staff at the RAF Croughton base.