London-based Privacy International has filed complaints with data protection and privacy authorities in 17 countries. The group says that financial transactions have been revealed to the US "without any legal basis or authority".
The US Treasury said on Friday that it has tracked millions of financial transactions handled by the Belgium-based Society for Worldwide Interbank Financial Telecommunication, or SWIFT, since the September 11, 2001, attacks. The operation is aimed at identifying people who are funding terrorist organisations.
SWIFT oversees 11 million financial transactions a day between banks and financial institutions worldwide, recording customers' names, account numbers and other identifying information.
Privacy International said the complaint had been sent to regulators in 13 countries in Europe, as well as Canada, Australia, New Zealand and Hong Kong. It asks authorities to "intervene to seek the immediate suspension of the disclosure programme pending legal review".
On Monday, George Bush criticised American newspapers which published details of the tracking programme, saying the reports made it "harder to win the war on terror".
Bush said the monitoring programme, run by the CIA and the treasury, had been authorised and Congress had been briefed. He said the disclosure by The New York Times was "disgraceful".
The newspaper said it refused government requests not to publish the story.
Officials said the programme had led to the capture of al-Qaeda operative Riduan Isamuddin, who is believed to have been involved in the 2002 bombings in Bali, Indonesia, and helped identify a US man convicted of helping an al-Qaeda member launder $200,000 through a Pakistani bank.
In December, The New York Times published a report revealing that Bush had authorised the National Security Agency to gather information on thousands of telephone calls made by Americans, without a warrant issued by a special court.
That disclosure also resulted in allegations that the paper was undermining US national security.