The US government is seeking to obtain private information on the accounts of Twitter users which it claims are linked to Wikileaks.
The orders were made by in secret, by a grand jury set up in Alexandria, Virginia.
The disclosure is intended to form part of an investigation determining whether a criminal case can be bought against Julian Assange, the founder of Wikileaks.
Also the subject of the investigation is US soldier Bradley Manning.
In court in Virginia, civil liberties lawyers have been arguing that the orders are unlawful, and that they must be made public.
A ruling on the issue is yet to be made.
Elsewhere, US Secretary of State Hillary Clinton has been praising internet freedom in a speech in Washington.
The Secretary of State cited examples of the uprisings in Egypt and Tunisia where social networking sites such as Facebook and Twitter have played key roles.
The importance of social networking sites was also highlighted by civil liberties lawyers contesting the disclosure orders.