Whistle-blower website and its volunteers report that US wants information from the micro-blogging platform.
WikiLeaks has said that its Twitter account details have been subpoenaed by the US government and that it hopes to fight the order.
The website said on Saturday that US investigators have gone to San Francisco-based Twitter Inc to demand private messages, contact information and other personal details of Julian Assange, the WikiLeaks founder, and three people associated with the secret-spilling website.
WikiLeaks blasted the court order, saying it amounted to harassment.
"If the Iranian government was to attempt to coercively obtain this information from journalists and activists of foreign nations, human rights groups around the world would speak out," Assange said in the statement.
The court order said the information sought was "relevant to an ongoing criminal investigation" and ordered Twitter not to disclose its existence to Assange or any of the others targeted.The order was unsealed "thanks to legal action by Twitter," WikiLeaks said.
Birgitta Jónsdóttir, a member of parliament in Iceland, said that Twitter notified her that it "received legal process requesting information regarding your Twitter account in [relation to WikiLeaks]."
"I have nothing to hide and have done nothing wrong - i have no intention to hand my information over willingly to DoJ [US department of justice]," she said on Twitter.
Jónsdóttir, a former WikiLeaks volunteer, said that she had "10 days to stop it [release of her Twitter information] via legal process before Twitter hands it over."
She told Al Jazeera that she continues to support WikiLeaks and will fight the court order.
"I have just spoken to the ministry of foreign affairs in Iceland and I have spoken to the ministry of justice and they're looking into this. They're taking it quite seriously," she said.
"I do quite a lot of travelling in relation to my work... I'm scheduled to go to the United States in June to speak at a seminar and I want to make sure that I can travel freely without being under the threat of being arrested or my computer or my phones being taken away."
'Protecting users' rights'
Twitter said in a statement: "We're not going to comment on specific requests, but, to help users protect their rights, it's our policy to notify users about law enforcement and governmental requests for their information, unless we are prevented by law from doing so."
The US is also seeking details about Dutch hacker Rop Gonggrijp and US programmer Jacob Appelbaum, both of whom have previously worked with WikiLeaks.
Appelbaum, whose Twitter feed suggested he was travelling in Iceland, said he was apprehensive about returning to the US.
"Time to try to enjoy the last of my vacation, I suppose," he tweeted.
Gonggrijp expressed annoyance that court officials had misspelled his last name, and praised Twitter for notifying him and others that the US had subpoenaed his details.
"It appears that Twitter, as a matter of policy, does the right thing in wanting to inform their users when one of these comes in,"' Gonggrijp said.
"Heaven knows how many places have received similar subpoenas and just quietly submitted all they had on me.'"
WikiLeaks also voiced its suspicion that other organisations, such as Facebook and Google, had also been served with court orders, and urged them to "unseal any subpoenas they have received".
Meanwhile, WikiLeaks also said that it suspected other US internet companies had been contacted by American officials as part of the investigation.
US officials have been examining possible charges against WikiLeaks and its staff following a series of spectacular leaks that have embarrassed officials and damaged Washington's image.
Source: Al Jazeera and agencies