The debate comes six weeks after a National Security Agency contractor divulged details of huge programmes that collect telephone and Internet data on millions of Americans and foreigners.
A handful of liberal Democrats have joined Tea Party conservatives in the House of Representatives in sponsoring an amendment to halt NSA surveillance of Americans who are not connected to an ongoing probe.
Republican congressman Justin Amash tweeted his thanks to House Speaker John Boehner for bringing the amendment -- which is tacked on to the defense spending bill under review -- up for open debate this week.
In addition to limiting the government's ability under the Patriot Act to collect such information, the bill also requires that secret Foreign Intelligence Surveillance Act (FISA) court opinions be made available to Congress and that summaries of those opinions be made public.
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House Democrats John Conyers and Jared Polis joined Amash's amendment, which they said "makes sure that innocent Americans' information isn't needlessly swept up into a government database."
"The recent NSA leaks indicate that the federal government collects phone records and intercepts electronic communications on a scale previously unknown to most Americans," they added.
The two Senators assured lawmakers the data-mining programme is under "strict controls" and has been authorised by all three branches of government.
Ever since details of the classified programmes were leaked in early June, Congress has "explored how the programme can be modified to add extra privacy protections without sacrificing its effectiveness" in rooting out terror suspects, they said.
"Any amendments to defund the programme on appropriations bills would be unwise.