Swift handles many of Europe's bank transfers
The EU plans to renew an agreement allowing US officials to scrutinise European citizens' banking activities under US anti-terrorism laws.
EU member states have agreed to let the European Commission negotiate new conditions under which the US will get access to private banking data.
US officials currently monitor transactions handled by Swift, a huge inter-bank network based in Belgium.
German politicians have voiced concern about the scope of US bank scrutiny.
The US wants to have access to a new European database that Swift is setting up in Switzerland. The US Treasury already has access to Swift's American database.
Tracking the funding of terror groups globally has been a priority for Washington since the 11 September 2001 attacks on the US.
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.
Swift's co-operation with US anti-terrorism investigators first came to light in 2006. The data-sharing agreement was struck in 2007 after European data protection authorities demanded guarantees that European privacy laws would not be violated.
Speaking on Monday, EU Justice Commissioner Jacques Barrot said "it would be extremely dangerous at this stage to stop the surveillance and the monitoring of information flows".
A senior member of Germany's ruling Christian Democrats (CDU), Wolfgang Bosbach, said any new agreement had to provide "certainty about data protection and ensure that the personal data of respectable people is promptly erased".
The leader of the liberal Free Democrats (FDP), Guido Westerwelle, said the proposal for data-sharing with the US "must be stopped".
The co-chairmen of the Greens in the European Parliament, Rebecca Harms and Daniel Cohn-Bendit, meanwhile accused EU foreign ministers of bypassing the assembly.
Mr Barrot said it was not a "question of giving the US a blank cheque".
"The US authorities would continue to temporarily access the relevant data only after legal verification and under strict judicial control," he added.