Virginia alleged that Jeffery Epstein and the recently-convicted Ghislaine Maxwell trafficked her into sexual abuse and exploitation.
Summing up his ruling, Judge Kaplan wrote: “For the foregoing reasons, defendant’s motion to dismiss the complaint or for a more definite statement is denied in all respects.
“Given the court’s limited task of ruling on this motion, nothing in this opinion or previously in these proceedings properly may be construed as indicating a view with respect to the truth of the charges or countercharges or as to the intention of the parties in entering into the 2009 Agreement.”
Virginia has alleged that she was expected to engage in sexual activity with Prince Andrew in London, New York and the US Virgin Islands. Prince Andrew has denied the allegations.
Virginia, formerly known by her maiden name Virginia Roberts, had made a settlement agreement in 2009 with the late Epstein, which was released on Monday 3 January, where the financier paid Virginia $500,000 to end a claim for damages.
She then agreed not to bring any future cases against any other "potential defendants", but it does not mention Andrew by name.
The prince's lawyers have argued that the deal means Virginia cannot sue the Duke of York.
But, her lawyer David Boise contested that and said the agreement is irrelevant to her complaint against Andrew.
Mr Boise told Judge Kaplan: "The only claim that is asserted that was made in Florida in the 2009 action that covered Prince Andrew was the third count which was to transport somebody for the purpose of illegal sexual activity.
"There is no allegation that Prince Andrew was the person transporting. There is no allegation that Prince Andrew fell into the category of people who were doing the trafficking. He was somebody to whom the girls were trafficked."
And Virginia's lawyer also described the royal as "somebody to whom the girls were trafficked" in the bombshell hearing.
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The Prince is said to be in a "difficult situation" by BBC royal correspondent Nicholas Witchell.
He said: "I think it leaves Andrew in a difficult situation to put it mildly, even if this case is dismissed and it might be thought that it was unlikely on the basis of the interventions that the judge made yesterday."
Judge Kaplan, who ruled on the latest part of the case, said he appreciated the "arguments and the passion" over the 2009 agreement Virginia signed with Epstein.
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