Swift handles many of Europe's bank transfers
A key committee of Euro MPs has moved to block the renewal of an agreement which allows US anti-terror officials to access Europeans' bank data.
The European Parliament's civil liberties committee recommended that the full parliament reject the interim nine-month deal between the EU and US.
MEPs said the deal negotiated by EU governments provided insufficient privacy safeguards.
The US can access the Swift money transfer system, based in Brussels.
The European Parliament plans to vote on the EU-US data agreement next Thursday.
The parliament's press service says that if MEPs block it, they will be making use of a new power under the Lisbon Treaty to veto international agreements.
The treaty for the first time gives MEPs real power to shape EU legislation in the area of justice and home affairs.
The US started accessing Swift data after the 11 September 2001 terror attacks on New York and Washington. But the fact that the US was secretly accessing such data did not come to light until 2006.
The Greens' home affairs expert, Jan Philipp Albrecht MEP, said that in backing the new deal the European Commission and EU governments had "not respected the fundamental criticism about the lack of sufficient protections with regard to privacy and the rule of law".
The leader of the Socialist group, Martin Schulz MEP, said: "We want a new and better deal with proper safeguards for people's privacy."
Tracking the funding of terror groups globally has been a priority for Washington since the 2001 attacks.
Swift handles millions of transactions daily between banks and other financial institutions worldwide. It holds the data of some 8,000 banks and operates in 200 countries.