The European Union is threatening to freeze a crucial and controversial data-sharing deal with the US aimed at tracking terrorist funding because of the National Security Agency snooping scandal.

Cecilia Malmstrom, the EU commissioner responsible for dealing with the fallout from the NSA and GCHQ disclosures, said she was unhappy with the information supplied by the US government and that the so-called SWIFT agreement of 2010 which supplies bank and credit card transaction data to the US treasury to help track terrorist funding may need to be suspended if the Americans were breaking the deal.

"I am not satisfied with what we have received so far," Malmstrom told a European parliament committee debating the NSA controversy. "Whilst from the US reactions last week we now have some understanding of the situation, we need more detailed information in order to credibly assess reality and to be in a position to judge whether the obligations of the US side under the agreement have been breached.

"A decision to maintain the agreement or to consider proposing its suspension is a serious matter. A decision to propose a suspension requires an objective and comprehensive assessment."

The terror finance tracking programme (TFTP) was agreed in 2010 under strong US pressure, requiring the EU authorities to transfer data to the US treasury from the Brussels-based system which collates global financial transaction data under the Society for Worldwide Interbank Financial Telecommunication (SWIFT).

MEPs on the committee called for the agreement to be scrapped following recent reports that the NSA was also tapping into the SWIFT databases to gain access to the private data of Europeans on their financial dealings.

The Dutch liberal MEP, Sophie in 't Veld, said the US breach of trust meant the transatlantic agreements, including another one divulging European air passenger details to the US authorities, should be ditched.

"For me the TFTP agreement is effectively dead ... null and void," she said.

The parliament, however, is not empowered to scrap the transatlantic agreements. Malmstrom and the European commission would need to conclude that the Americans were in breach, propose a suspension of the agreement, and then the 28 governments of the EU would need to agree. That could prove a tall order.

Malmstrom said the decision would need a qualified majority among EU governments, meaning that Britain would not have a veto. With Britain's GCHQ heavily involved in the European snooping and surveillance operations, the UK is in an awkward position, both in the EU but also party with the US in the controversy.

Senior EU officials and a SWIFT executive denied the reports that the NSA was grabbing the financial data, or said there was insufficient evidence to level the allegation. But Malmstrom emphasised that it was up to the Americans to clear their own names with adequate information.

"We simply have no evidence," Rob Wainwright, the head of Europol, the EU's police agency, told the committee. But that lack of evidence was because Europol had not investigated the allegations. Wainwright said the agency had no mandate to do so, was not in contact with any of the key US agencies and had not been asked by any EU government to get pro-active on the NSA scandal.

SWIFT's top lawyer, Blanche Petre, told the committee that the organisation had "no reason to believe that there has been an unauthorised access to our data."

Malmstrom disclosed that her department was examining how well the TFTP programme with the Americans was working, but that the inquiry had been frozen "in light of recent developments."

• This article was amended on 25 September 2013. An earlier version quoted Malmstrom as saying a decision to suspend the deal would need to be unanimous among EU governments. In fact she said a qualified majority would be needed.