David Boies, for Ms Giuffre, maintained that Prince Andrew had been served when the papers were delivered to his home at Royal Lodge, Windsor on August 27.
“We’ve proceeded to serve Prince Andrew in several ways pursuant to Article 10 of the Hague Convention,” he told the judge.
Judge Kaplan concluded that Prince Andrew would have the papers served on him at some point, either through Mr Brettler or via the UK Central Authority.
He scheduled the next conference for October 13, giving Ms Giuffre’s legal team time to find an alternative method of service.
Mr Brettler was instructed by Prince Andrew within the last fortnight and applied to take part in the court hearing just hours before it was due to start.
The lawyer has represented several men facing sexual assault charges, including Hollywood actor Armie Hammer, comedian Chris D’Elia, who was accused of soliciting child pornography from 17-year-old girl, and Hollywood director Bryan Singer.
Mr Hammer is currently under investigation by the Los Angeles Police Department after being accused by a 24-year-old woman of violent rape and physical abuse throughout their four-year on-and-off relationship.
Several other anonymous women also came forward with accusations of sexual impropriety.
Mr Brettler has denied the allegations on his behalf, claiming all of their interactions were “completely consensual”.
Ms Giuffre, claims she was forced to have sex with the Duke three times when she was aged 17 in New York, London and the US Virgin islands. She is suing him under New York’s Child Victims Act. The Duke denies the claims and says he has “no recollection” of meeting her.