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At a committee hearing last week to examine the NSA's programs, Feinstein outlined her plans for the bill.

She said the legislation would tweak — but not end — the NSA’s controversial program to collect records on all U.S. phone calls.

She said the bill would also require that the Senate confirm the NSA director and would instruct the agency to produce annual reports containing statistics on its surveillance activities.

Sens. Ron Wyden Ronald (Ron) Lee WydenGOP senator blocks Schumer resolution aimed at Biden probe as tensions run high Republican Senators raise concerns over Oracle-TikTok deal Hillicon Valley: TikTok, Oracle seek Trump's approval as clock winds down | Hackers arrested for allegedly defacing U.S. websites after death of Iranian general | 400K people register to vote on Snapchat MORE (D-Ore.) and Mark Udall Mark Emery UdallThe 10 Senate seats most likely to flip Democratic presidential race comes into sharp focus Democrats will win back the Senate majority in 2020, all thanks to President Trump MORE (D-Colo.), vocal civil liberties advocates, had been expected to push more aggressive privacy protection proposals as amendments to Feinstein's bill during the markup.

A coalition of privacy advocates and other organizations sent a letter to Feinstein on Monday, urging her to make the markup open to the public.

—Updated at 5:35 p.m.