Speech test
The American Civil Liberties Union (ACLU) and the Electronic Frontier Foundation are planning to "intervene" for Wikileaks at the continuation hearing.
The rights groups claim the order that knocked Wikileaks offline in the US raises "serious First Amendment concerns".
"Blocking access to the entire site in response to a few documents posted there completely disregards the public's right to know," said ACLU attorney Ann Brick in a statement.
The order granted for Julius Baer by US district judge Jeffrey White ordered Dynadot - the company that hosts the Wikileaks website in America - to remove all mentions of the site from its address books.
Anyone in the US trying to find Wikileaks would have to consult this address list to find the website.
The bank took the action in mid-February because, it is understood, the documents hosted could have had an impact on a separate case being heard in Switzerland.
Julius Baer said the case had nothing to do with free speech.
"This action has been brought solely to prevent the unlawful dissemination of stolen bank records and personal account information of its customers," lawyers for the bank wrote in court papers.
"Many of those documents have also been altered and forged," said the legal filing.
However, the attempt to get the documents removed spurred many other sites to host them and Wikileaks' sites in other countries were largely unaffected by the ruling.
The US site itself was also reachable by those that knew its numerical net address rather than just its English name.
In total, 18 organisations have pledged support for Wikileaks in documents filed to the US court that will hear the legal argument.