The order calling on Twitter to release data about the accounts of Icelandic lawmaker Birgitta Jonsdottir, US computer researcher Jacob Appelbaum and Rop Gonggrijp, a Dutch volunteer for WikiLeaks, was handed down in December by Judge Theresa Buchanan.
Buchanan, who also heard Tuesday's challenge, ordered Twitter in December to hand over to the US government information on the three subscribers and any other clients linked to WikiLeaks, the organization led by Julian Assange that last year released a slew of US diplomatic cables.
Among the information Twitter was ordered to give to the government were Internet Protocol addresses and the names and addresses of "tweet" recipients.
The December court order was sealed -- or secret -- until last week, when the details were made public to allow Jonsdottir, Appelbaum and Gonggrijp the right to reply.
In a tweet sent to AFP, Jonsdottir said she was determined to fight for her right and the right of "other social media users" to privacy.
"I don't have much choice, do I -- nor other social media users," she said when asked if she would hand over her Twitter account details to the US authorities.
"That's why this has to be fought and discussed."
