The family is taking legal action against the foreign secretary after their son was killed in a collision outside an RAF station in Northamptonshire.
They have claimed Mr Raab misused and abused his power when he granted diplomatic immunity to Anne Sacoolas, the crash suspect whose husband is a US diplomat.
The Foreign Office has said it will oppose the family’s legal action and it will "seek costs for doing so.”
Mr Raab defended the decision by saying the government needs to “protect taxpayers’ money” by opposing the case.
“We just cannot responsibly allow ourselves to be sued without taking the normal action in defending ourselves when the position that the representative and the family are pursuing in law is wrong,” the foreign secretary told Sky News.
“It pains me because I want to give them the solace of justice in this case.
“But we also need to protect the taxpayers' money and the legal position that we set out, which is the correct one.”
Ms Sacoolas is thought to have been driving on the wrong side of the road when her car hit Mr Dunn.
In October, the Foreign Office announced that diplomatic immunity no longer applied following her return to the US.
The Dunn family has set up a crowdfunding campaign which has raised £90,000 of its £100,000 target since being created on 1 October.
Radd Seiger, the spokesperson for the family, said the parents were “livid” at Mr Raab’s comments.
“[The family] are not engaged in some frivolous vexatious litigation frolic of their own against the FCO,” Mr Seiger said.
“Quite the opposite. They are British citizens who have had their entitlement to justice robbed from them by the US government under the watch of Mr Raab and the FCO.
“He knows perfectly well that Ms Sacoolas never had diplomatic immunity.”
Mr Seiger also claimed the foreign secretary had “lied to the parents” and was now “lying to the nation”.
He added: “If he is so concerned about taxpayers' money in the litigation then he would come and talk to us to find a resolution, rather than risking having to have the taxpayers themselves having to pay a very expensive legal bill if the FCO lose."
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