If approved by Parliament, the Investigatory Powers Bill will give police and spies broad powers to obtain Internet connection records, a list of websites, apps and messaging services someone has visited, though not the individual pages they looked at or the messages they sent.
It will also require telecommunications companies to keep records of customers' Web histories for up to a year and to help security services gain access to suspects' electronic devices.
Committee chairman Paul Murphy, a Labour member of the House of Lords, said the bill had many positive features, but the government "has a significant amount of further work to do before Parliament can be confident that the provisions have been fully thought through."
Earlier this week another group of lawmakers, the Intelligence and Security Committee, said the bill did too little to protect individuals' privacy.
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Internet companies including Facebook, Google, Microsoft, Twitter and Yahoo have also raised concerns. The firms are especially concerned that the measures could weaken encryption, which is key to ensuring online shopping and other activities can be conducted securely.
Today's report said the bill should make it explicit that firms will not be expected to provide decrypted copies of communications "if it is not practicable for them to do so."
Home Secretary Theresa May said the government would "carefully consider" the committees' recommendations before setting out final proposals in the spring.