Prime Minister Boris Johnson says he and President Biden are "working together" to end the row over whether Anne Sacoolas should face trial over the death of 19-year-old Harry Dunn.
Ms Sacoolas claimed diplomatic immunity after the teenager died when her car hit his motorbike almost two years ago.
Speaking at the G7, Mr Johnson said the president was "extremely sympathetic" and "actively engaged" in the case.
Mr Dunn's mother Charlotte Charles said she "couldn't be more grateful".
She said: "It means a tremendous amount that the first time that Mr Johnson gets an opportunity to meet President Biden face-to-face he raises Harry."
Mr Dunn died in August 2019 after Ms Sacoolas's car struck his motorbike, moments after she left the RAF base in Northamptonshire where her husband worked for a US intelligence agency.
His mother said the conversation seemed to be a "significant development" but she was "anxious to await further information" and to see "exactly where the comments made yesterday will lead to".
"My hope as always, my family's hope as always, is to ensure that I can complete my promise to Harry. We will not rest until justice is done," she said.
She said she hoped President Biden, who lost his first wife, Neilia Hunter, and their one-year-old daughter Naomi in a car crash in 1972, would be "sympathetic".
"When someone has experienced such a tragic loss as he has, we've always hoped that he would be able to understand why justice is so important to us."
The family wants Ms Sacoolas to be stripped of diplomatic immunity in order to face a British court over the death.
She flew home days after the crash, when Washington told London that she had diplomatic immunity - meaning there could be no criminal prosecution.
Those international rules protect officials and their families from unjust interference from host nations while they are stationed abroad.
The Crown Prosecution Service disagreed and issued an extradition request, saying Ms Sacoolas must face trial for causing Mr Dunn's death by dangerous driving, an offence which can lead to a maximum sentence of 14 years.
Former President Donald Trump's administration rejected the extradition request and refused to waive Ms Sacoolas' diplomatic immunity, which Mrs Charles said had left "quite deep emotional scars".
Speaking to BBC political editor Laura Kuenssberg at the G7 in Cornwall, Mr Johnson confirmed he and President Biden were now "working together" - although he stressed that "legal processes" had to be allowed to take their course.
"I have to say that you should really, when you get the chance, put your question to the president because he is actively engaged in the case," said the prime minister. "He has his own personal reasons for feeling very deeply about the issue."
Mr Johnson continued: "He was extremely sympathetic, but this is not something that either government can control very easily because there are legal processes that are still going on.
"I think the difficulty is that there are limits to what the executive can do with the legal, with the judiciary and the legal system, but both sides are working together."
While Mr Dunn's parents wait for the possibility of justice via a criminal trial, a senior judge in the US has given them permission to sue Anne Sacoolas and her husband, Jonathan.
Mrs Charles said the family was "tired but we're not going to rest until justice is done".
"It doesn't get any easier, we're still not living with those scars yet because we're still yet to really grieve," she added.