Snowden said the powers given to security agencies in the bill amounted to access to “the activity log of your life.”
Earlier, the Home Secretary Theresa May admitted that UK spy agencies MI5, MI6 and GCHQ secretly collected communications data for decades to protect “national security.”
May announced on Wednesday that internet companies would be required to store a record of every website accessed by users for a year.
The new bill also targets encrypted messaging services, such as WhatsApp and iMessenger, which allow users to evade hackers and data collection.
Snowden began leaking classified intelligence documents in June 2013, revealing the extent of the NSA’s spying activity.
He revealed that the spy agency has been collecting the phone records of millions of Americans and foreign nationals as well as political leaders around the world.
Snowden fled his country to avoid espionage charges and was granted asylum in Russia, where he currently resides.
Moscow’s decision to grant temporary asylum to Snowden was a major factor in the deteriorating US-Russian relations, which have declined to Cold War lows over the ongoing conflict in Ukraine.
Many Americans regard Snowden as a whistleblower and a national hero for blowing the lid off the US government’s global surveillance operations.