"Concerns have been expressed over surveillance regimes adopted by some states without adequate safeguards to protect individuals' right to privacy," Pillay told a UN counter-terrorism conference in Geneva.
"If our goal in countering terrorism is to provide for the security of individuals and preserve the rule of law, such practices are... Counterproductive," she said.
Her comments came shortly before the FBI announced it had launched a criminal investigation against an American government subcontractor after he exposed a massive US surveillance operation.
The NSA said date from the programme had thwarted dozens of potential attacks.
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But Swiss Foreign Minister Didier Burkhalter told conference: "The quest for security must not lead to excessive infringements of the right to privacy."
Switzerland this week asked Washington for explanations about Snowden's revelations, especially on an alleged CIA blackmail operation to spy on its banks while he was stationed in Geneva as a diplomatic attache from 2007 to 2009.
"Would we have a better society if honest citizens were subjected to constant surveillance by governments, with all the abuses that this may bring?" Burkhalter said. "In Switzerland's view, the answer is definitely no."
"When the principles enshrined in the human rights instruments are disrespected, extremism tends to thrive," said Feltman, who heads the world body's Counter-Terrorism Implementation Task Force Office (CTITF).