The suspect, the wife of a US intelligence official, claimed diplomatic immunity after the collision and was able to return to her home country, sparking an international controversy.
The Home Office said it submitted the request for Anne Sacoolas on Friday after she was charged with causing the 19-year-old’s death by dangerous driving last month.
Mr Dunn died after his motorbike crashed into a car outside RAF Croughton in Northamptonshire on August 27 last year.
The Prime Minister told BBC Breakfast: "I think that it's right that we made the appeal for extradition."
But he added: "I think the chances of America actually responding by sending Anne Sacoolas to this country are very low. That's not what they do."
Reacting to the prime minister's comments from Denver in the US, the Dunn family spokesman Radd Seiger said: "I do not know what is in the prime minister's mind in making those comments because the parents and I have not yet had the opportunity to sit down and talk with him - but we expect to do so within the next few days.
"Certainly, if he is basing those comments on what is currently emanating from Washington he may well be right.
He added the family will take things "one step at a time" and said his view on the chances of success is "diametrically opposed to Mr Johnson's".
"If that is what transpires, the campaign will swing into action deploying a number of measures including blockading the bases and will sit down with British officials to discuss what they will do, not only on Harry's family's behalf, but the whole nation's to ensure that justice is done and that no-one ever suffers the same fate as Harry," he said.
"That is not a sustainable position and I have made that crystal clear to the Government and the point has been taken on board.
"But we will take one step at a time and not get ahead of ourselves. Anne Sacoolas will be coming back to the UK to face justice. Unlike the Prime Minister, there is no doubt in my mind."
The US Department for State has said it has always been their position that Mrs Sacoolas had diplomatic immunity, stating that a request to extradite somebody with immunity would be an abuse.
A spokesman said the United States has a strong law enforcement relationship with the UK and, in particular, a strong track record of close cooperation on extradition matters but, under the circumstances of this case, they strongly believe that an extradition request would be highly inappropriate.
The spokesman added that they will continue to engage with the UK government and said they have been transparent on all matters, both legal and diplomatic.