The two sides have been negotiating for four years over the agreement that would protect personal data exchanged between police and judicial authorities in the course of investigations, as well as between companies and law enforcement authorities.
However, talks have been hampered by the lack of a right for non-resident EU citizens in the US to go to US courts if they believe their data has been misused or unlawfully disclosed.
The European Commission has said the agreement cannot be signed and formally concluded until the right to judicial redress for EU citizens is enshrined in US law.
The document says the bill appears to have received bipartisan support, and if passed would restore trust in frayed trans-Atlantic relations after allegations of mass US spying emerged in 2013.
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