In remarks that opened the 23rd session of the Human Rights Council in Geneva, Pillay said, "I come to this task today in the hope that we will be able to spark tangible action to stop the escalating bloodshed and suffering in Syria, which after 26 months has become an intolerable affront to the human conscience."
"What began as non-violent protests has spiraled into a brutal and increasingly sectarian civil war, to some extent fueled by external actors," she said. "Civilians bear the brunt of this crisis in which human rights violations have reached horrific dimensions. Confronted with the flagrant disregard of international law and human life on every side, I feel utter dismay."
She said the International Criminal Court must mete out justice to those who've violated the rights of Syrians since the civil war began as peaceful protests against President Bashar Assad in March 2011.
"These war crimes and crimes against humanity cannot be allowed to go unpunished," Pillay said. "We must make it clear to both [the Assad government] and the armed opposition groups that there will be consequences for those responsible. And the world must take action to end this terrible conflict."
Russia -- which has blocked anti-Assad efforts at the United Nations -- and the United States have renewed diplomatic efforts to start peace talks between the Assad regime and the opposition. Damascus agreed "in principle" to participate in the conference Sunday in Geneva.
In Syria, 35 people were killed, including two women and two children, the opposition Local Coordination Committees in Syria said.
In Brussels, meanwhile, British Foreign Minister William Hague urged the European Union to end its arms embargo to Syria Monday so EU members could supply weapons to some rebels.
The foreign ministers struggled Monday to find agreement about whether to allow weapons to be sent to the Syrian opposition, as some insisted the rebels need arms to avoid being massacred and others warned that relaxing the current embargo could prolong the bloodshed, The Wall Street Journal reported.
Britain and France have been urging the European Union to lift the ban on sending weapons to the main opposition group.
The current Syria arms embargo expires June 1. Failure to extend the ban or amend it before it expires would open the way for weapons to be sent to all sides in the Syria conflict, The Wall Street Journal said.
"Let me emphasize, we're looking for common ground in this meeting," British Foreign Secretary William Hague told reporters Monday morning before talks in Brussels began. "[How] long can we go on with people having every weapon that's ever been devised dropped on them, while most of the world denies them the means to defend themselves?"
Britain maintains that amending the arms ban to EU members to send weapons to certain rebels would be key to force Assad to take peace talks seriously. Others counter that such a step could derail the coming peace conference or provide Assad with an excuse not to attend.
"Austria, and its government, is clearly against lifting the weapons embargo," said Austrian Foreign Minister Michael Spindelegger. "We aren't blocking anything but saying let's continue this path toward a political solution. Supplying weapons ... will lead to an arms race, not peace."
Dutch Foreign Minister Frans Timmermans confirmed the Netherlands and Germany are leading the effort to try to forge a compromise within the EU community, the Journal said.
The Journal said options being examined include one that would allow the main Syrian rebel group to receive weapons uniquely for protecting civilians and a short extension of the arms ban to give EU ministers time to see how peace talks progress.
The French newspaper Le Monde reported chemical weapons were frequently used by the Syrian government against the rebels.
The account, the culmination of a two-month undercover reporting assignment, said chemical weapons were used on several consecutive days in an area near Damascus that rebels entered in January.
Although there was no indication that a toxic gas was released, victims suddenly exhibited symptoms such as violent coughing, burning eyes and blurred vision.