"I think it's not just my office but anybody is entitled to know exactly what happened," she added.
Pillay's declarations come a day after US Attorney General Eric Holder told a Senate hearing the raid during which bin Laden was killed "was lawful and consistent with our values."
"The United Nations condemns terrorism but it also has basic rules of how counter-terrorism activity has to be carried out. It has to be in compliance with international law," she said.
"For instance, you're not allowed (...) to commit torture or extra-judicial killings," she explained.
The White House's changing story over the attack has raised doubts about US assurances that the US special operations forces sent to bin Laden's lair in the Pakistani garrison town of Abbottabad were prepared to take him alive.
"If he had surrendered, I think -- attempted to surrender -- I think we should, obviously, have accepted that," Holder told the Senate committee.
Pillay said this week "the United States has clearly stated that their intention was to arrest bin Laden if they could, I fully understand that this was always likely to have been difficult."
On Monday, the White House said bin Laden was armed when he was shot dead in his comfortable compound not far from Islamabad.
But a day later, White House spokesman Jay Carney corrected that account, saying the terror chief was unarmed when gunned down by an elite team of US Navy SEALs in what he called a "highly volatile firefight."