Pillay's office said Friday at least 13 people have died and another 140 people were injured in political violence that erupted in early February.
"It is time for all sides to move beyond verbal aggression and towards meaningful dialogue," she said in a statement. "This crisis will only be resolved if the human rights of all Venezuelans are respected."
National unrest grew out of public frustration with declining economic health in the oil-rich Latin American country. It's since spilled over into the political arena with President Nicolas Maduro accusing his opponents of getting support from the U.S. government.
Pillay said, however, all parties to the violence needed to show restraint and sit down together at the negotiating table.
"The inflammatory rhetoric from all sides is utterly unhelpful and risks escalating the tense situation in the country," she said.
The European Parliament expressed its concern over the lack of fundamental rights in Venezuela.
"Venezuelan authorities must ensure the security of all, immediately disarm and dissolve the uncontrolled armed pro-government groups and end their impunity," it said Thursday.