A senior U.S. Senate Republican took a swipe on Wednesday at an effort to forge a new deal on the movement of electronic data between the United States and Europe, such as Facebook user information, but it was unclear if he had jeopardized the unfinished pact.

Seen as crucial to preserving the free flow of data across the Atlantic, an issue for thousands of companies, the Safe Harbor data-transfer agreement being negotiated in Brussels is days away from an important deadline.

Amid growing concerns in Europe about spying by U.S. authorities on Internet data, a previous agreement was invalidated in October 2015 by an EU court. The new agreement would replace that pact.

The U.S. Senate is debating related legislation, the Judicial Redress Act, and Senator John Cornyn of Texas told Reuters in an interview he would try to amend that legislation.

"I’m for doing what’s in America’s best interests, not necessarily the interests of the European Union," said Cornyn, the Senate's No. 2 Republican.

“I’m going to make sure ... that we don’t just try to do something to help them out and we don’t protect our interests.”

The Act would allow citizens of U.S. allies in Europe to sue over data privacy in the United States. It will be considered on Thursday in a Senate committee, an aide said.

It not seen as crucial to securing a new Safe Harbor deal, but its passage would send a signal of good faith to negotiators in Brussels as they scramble to meet a deadline, European officials and technology trade groups said.

That message could be upended by amendments from Cornyn and Republican Senator Orrin Hatch of Utah. One would limit the ability to sue in U.S. courts to citizens of countries already in an international data deal with the United States, such as Safe Harbor, sources familiar with the language said.

Another possible amendment would require the U.S. attorney general to certify that participating countries do not have policies that impede U.S. national security.

Thousands of firms, such as Google and Microsoft, relied on the 15-year-old Safe Harbor for freely transferring trans-Atlantic data.

EU data protection authorities gave negotiators until the end of January to strike a new deal before potentially moving forward with lawsuits.

"Time is not on our side," Justin Antonipillai, a Commerce Department official, said at a conference in Washington this week.

(Editing by Kevin Drawbaugh and Grant McCool)