A group of MEPs has appealed to US homeland security chief Michael Chertoff to declassify a report on the use of EU airline passenger data.
Passengers details are sent to the US 72 hours before take-off
The report has been shown to members of the parliament's civil liberties committee in a locked room.
It evaluates the implementation of an agreement under which, since May 2004, the EU has sent the US details of passengers on transatlantic flights.
The European Commission has also sought permission to make parts of it public.
The letter from four Liberal MEPs on the committee expresses "deep concern" at the confidential treatmtent given to the report, at the request of the Department of Homeland Security.
"We feel that our citizens have a right to know if their personal data are safe with the US authorities, if the Passenger Name Records scheme is effective from a security point of view (ie if it has demonstrably led to greater security) and if both parties fully comply with the undertakings in the agreement," they add.
The deal on Passenger Name Records (PNR) is designed to help avert acts of terrorism, but the European Parliament is concerned personal data could be misused.
Under European data protection rules, such information can only be passed to a third country if its data protection regime is judged to be adequate by the European Commission.
The commission decided the US data protection regime was adequate, but MEPs disagreed.
Officials from the US, the European Commission and some EU national governments reviewed the implementation of the agreement in September and wrote a joint report in December.
The report was discussed by the parliament's civil liberties behind closed doors on Monday.
"We are unhappy with this confidentiality in principle, but also because we believe that we have a right to let our citizens know what is the state of affairs on US compliance with undertakings that they signed up to," Baroness Sarah Ludford told the BBC News website.
"It's a matter of serious public interest, what is in this document."
The other signatories of the letter to Mr Chertoff are Sophie in't Veld and Jeanine Hennis-Plasschaert from the Netherlands, and Alexander Alvaro from Germany.
In November, an adviser to the European Court of Justice rejected the parliament's argument that handing the data to the US was a breach of citizens' privacy.
However, he advised scrapping the deal on the grounds that the EU did not have the authority to agree to it.
The court itself has yet to give its ruling.