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The new version of the legislation, S. 3342, aims to address the concerns of privacy advocates, who had warned that the old bill would give spy agencies access to Americans' private online information.

The Republican senators said their new bill tightens the definition of "cyber threat information" and clarifies that the government cannot use or retain the information for reasons other those specified in the bill. They also said it creates new oversight authorities to protect privacy and civil liberties.

Hutchison said the lawmakers worked closely with interest groups to draft the new version of the bill, and they believe the new Secure IT is a "consensus bill that will significantly advance the security of our government and private sector networks."

“Our bill focuses on giving companies and the government the tools and knowledge they need to protect themselves from cyber threats, and creates new important requirements for government contractors to notify their agencies of significant cyber-attacks to their systems,” she said in a statement.

Importantly, the bill still does not give the government any power to set mandatory security standards for critical infrastructure systems.

The White House and Senate Democrats argue that standards for critical systems, such as electrical grids and gas pipelines, are a necessary part of any cybersecurity legislation. They argue that without mandatory standards, the country will be at risk for a devastating attack that could cost thousands of lives.

A separate bill offered by Sens. Joe Lieberman (I-Conn.) and Susan Collins Susan Margaret CollinsThe Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power Billionaire who donated to Trump in 2016 donates to Biden Credit union group to spend million on Senate, House races MORE (R-Maine) would empower the Homeland Security Department to set cybersecurity standards. But Republicans argue security mandates would burden business and do little to improve cybersecurity.

"The key to successfully fighting this threat is not adding more bureaucrats or forcing industries to comply with government red-tape,” McCain said in a statement. “Instead, we must leverage the ingenuity and innovation of the private sector in partnership with the most effective elements of the federal government to address this emerging threat.”

In an email, Leslie Phillips, a spokeswoman for Lieberman, said the senator is "encouraged that Republicans recognize the urgency of cybersecurity and looks forward to a lively floor debate."

"He is, however, disappointed that SECURE IT does not address the grave threat of cyber attack against critical infrastructure," she said.

The Secure IT Act is also co-sponsored by Sens. Chuck Grassley Charles (Chuck) Ernest GrassleyGOP lawmakers distance themselves from Trump comments on transfer of power The Hill's 12:30 Report: Ginsburg lies in repose Top GOP senators say Hunter Biden's work 'cast a shadow' over Obama Ukraine policy MORE (R-Iowa), Lisa Murkowski Lisa Ann MurkowskiOVERNIGHT ENERGY: House passes sweeping clean energy bill | Pebble Mine CEO resigns over secretly recorded comments about government officials | Corporations roll out climate goals amid growing pressure to deliver The Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Abortion stirs GOP tensions in Supreme Court fight MORE (R-Alaska), Dan Coats Daniel (Dan) Ray CoatsFBI chief says Russia is trying to interfere in election to undermine Biden The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump, Biden renew push for Latino support Former Intel chief had 'deep suspicions' that Putin 'had something on Trump': book MORE (R-Ind.), Ron Johnson Ronald (Ron) Harold JohnsonThe Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' The Hill's 12:30 Report: Ginsburg lies in repose CHC leaders urge Senate to oppose Chad Wolf nomination MORE (R-Wis.) and Richard Burr Richard Mauze BurrHillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Bipartisan representatives demand answers on expired surveillance programs Rep. Mark Walker says he's been contacted about Liberty University vacancy MORE (R-N.C.).

Senate Majority Leader Harry Reid Harry Mason ReidThe Supreme Court vacancy — yet another congressional food fight Trump seeks to turn around campaign with Supreme Court fight On The Trail: Battle over Ginsburg replacement threatens to break Senate MORE (D-Nev.) has said he plans to bring the Lieberman-Collins bill to a vote next month.

Sens. Sheldon Whitehouse Sheldon WhitehouseThe Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Feinstein 'surprised and taken aback' by suggestion she's not up for Supreme Court fight Hillicon Valley: Murky TikTok deal raises questions about China's role | Twitter investigating automated image previews over apparent algorithmic bias | House approves bill making hacking federal voting systems a crime MORE (D-R.I.) and Jon Kyl (R-Ariz.) are working on a compromise that would pressure, but not force, critical infrastructure systems to better protect their systems.

—Updated at 2:10 p.m.