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Home Office Minister James Brokenshire has said he will listen to concerns on the 'snooping bill' but added there is an urgency to get it through to protect the public.
Nick Clegg acknowledged that new powers were needed by the law enforcement agencies to fight crime, but said they must take account of the committee's concerns.
The committee said under the draft Bill, the Home Secretary would be given "sweeping powers to issue secret notices" ordering communications companies to disclose "potentially limitless categories of data".
Ministers argue that proposal, known as clause one, has been kept deliberately wide so it can be "future-proofed".
But the committee dismissed the argument and criticised the Government for failing to properly take account of the right to privacy.
Government plans to give the police and security services new powers to monitor all emails, web visits and phone calls must undergo a "fundamental rethink", Nick Clegg has warned.
The Deputy Prime Minister said ministers needed to "go back to the drawing board" after a committee of MPs and peers found measures supposed to enable investigators to keep pace with technological developments went far further than necessary and amounted to overkill.
The committee, set up to examine the draft Communications Bill, accused the Government of using "fanciful and misleading" figures to support its case for the legislation.
Mr Clegg said ministers must take account of the committee's findings and that the Bill - dubbed a "snooper's charter" by critics - could not proceed in its current form.
Latest ITV News reports
The Government's draft Communications Bill is to be re-written after a Commons Committee branded it 'overkill'.