The committee issued a statement on Monday expressing concerns over possible privacy and data protection violations within Europe's Swift financial transition network.
US officials have been requesting bank and transfer information for years as a way to trace funding from individual donors and organisations to terrorist groups. The programme is said to date as far back as 2006.
Members of the European Parliament are now pressing US and European officials to draft a new agreement which provides stricter protections and tighter control by EU authorities.
"Private companies are having to grapple with a difficult situation. We cannot just leave them to it," said MEP Timothy Kirkhope. "We must ensure that data is not transferred on the basis of criteria which are not ours."
The question of government access to account and transfer information has become a hot topic over the past decade, as governments attempted to dissect and dismantle funding sources for global terrorism networks.
While the information has been vital in cutting off funding for terrorist groups, many have argued that the investigations put personal information at risk, and place many banks in the difficult position of having to hand over data which would otherwise be tightly guarded.