Republican Congressman, Peter King, called the actions of the leading US newspaper "disgraceful" and said he believed it had violated counterespionage laws.
Congressman King is chairman the House Committee on Homeland Security which looks into issue of national security.
"The New York Times is putting its own arrogant, elitist, left-wing agenda before the interests of the American people," Congressman King said on "Fox News Sunday".
"And I'm calling on the attorney general to begin a criminal investigation and prosecution of the New York Times, its reporters, the editors that worked on this, and the publisher," he said.
The Times was among a group of several US newspapers that on Friday reported that the US government had secretly monitored scores of banking transactions around the globe since the September 11, 2001 attacks on New York and Washington in order to track suspected terrorists.
The searches involved millions of records held by the Belgium-based Society for Worldwide Interbank Financial Telecommunication (SWIFT), an international cooperative that serves as a clearing house for the transactions.
The cooperative serves 7,800 financial institutions in more than 200 countries. Its database has reportedly provided valuable information about ties between suspected terrorists and groups financing them.
Hambali link
The information directly led to the capture of suspected Al-Qaeda operative Riduan Isamuddin, better known as Hambali.
Hambali was believed to be the key coordinator between Al-Qaeda and the radical group Jemaah Islamiyah.
Hambali has also been suspected of being the mastermind behind the 2002 Bali bombings in which more than 200 people died.
Officials say the database has also helped identify a US man convicted of helping an Al-Qaeda member launder US$200,000 through a Pakistani bank.
Members of President George W Bush’s administration have expressed disappointment that the secrecy surrounding the program has now been blown. But they stopped short of advocating legal action against The NY Times.
Congressman King said The NY Times had "compromised America's antiterrorist policies" for the second time in less that a year.
Last December, the paper published a report saying that Mr Bush had authorised the National Security Agency to listen in to thousands of telephone calls made by Americans without a warrant issued by a special counterintelligence court.
That disclosure had also prompted charges that the paper was undermining US national security.