Boris Johnson has said the government would do "whatever we can to get justice" for Harry Dunn, but would not commit to meet the teenager's parents.
Mr Dunn, 19, died when his motorbike was in a crash with a car near RAF Croughton, Northamptonshire, in 2019.
The suspect, Anne Sacoolas, later left for the United States on grounds of diplomatic immunity.
The prime minister said the government continued "at the highest level to raise this with the United States".
Mrs Sacoolas, the wife of a US intelligence official based at RAF Croughton, was charged with causing death by dangerous driving.
But a Home Office extradition request was refused by former President Donald Trump's Secretary of State Mike Pompeo in January last year.
More on Harry Dunn:
On a visit to Teesside with the Chancellor Rishi Sunak, the prime minister was asked by broadcasters if he would "publicly say" he would meet with Mr Dunn's family.
Mr Johnson said: "I've got massive sympathy with Harry Dunn's family and all his friends and everybody bitterly regrets what happened.
"I know that the foreign secretary has only recently raised it with Tony Blinken, the US Secretary of State.
"We will continue to do whatever we can to get justice for Harry Dunn."
The prime minister has yet to meet Mr Dunn's family, who have previously only met with the Foreign Secretary Dominic Raab about the case.
He said the government would "persevere" over the extradition of Mrs Sacoolas.
Mr Dunn's mother, Charlotte Charles, had previously said she had "renewed hope" for extradition following the election of US President Joe Biden.
But a State Department spokesman for the Biden administration said in January the decision to refuse extradition was "final".