She told reporters she had given the new toll of more than 5,000 dead -- including some 300 children -- and recommended that the crackdown by Assad's regime be referred to the International Criminal Court.
"The widespread and systematic nature of the killings, the detentions and the acts of torture -- I felt that these acts constituted crimes against humanity," said Pillay.
The "intolerable" situation in Syria -- where more than 14,000 people have been detained -- has seen 12,400 flee into neighbouring countries since protests erupted in March, she said.
"Inaction by the international community will embolden Syrian authorities, and ensure perpetrators go unpunished," Pillay said.
The Security Council meeting came as Western nations ramp up pressure to condemn Assad's campaign.
"Frankly we think that it is past time for the UN Security Council to speak up," State Department spokeswoman Victoria Nuland told reporters, denouncing Security Council silence on the Syrian regime as "unconscionable."
"And we are again calling on our partners on the Security Council to be willing to take action and speak out for the innocents in Syria who are suffering at the hands of the regime, including Russia," Nuland said.
Her comments echoed earlier remarks from German Foreign Minister Guido Westerwelle, who said council members resisting action against Damascus needed to "change their mind."
France's UN envoy Gerard Araud said the council was "morally responsible" for the daily deaths by staying silent.
But Syrian ally Russia said Western accusations that it was blocking UN action condemning the crackdown were "immoral" because the West was refusing to put pressure on armed rebel groups.
"There are those who refuse to put pressure on the armed, extremist part of the opposition and are at the same time accusing us of blocking the UN Security Council's work. I would call this position immoral," Foreign Minister Sergei Lavrov said in televised comments.
Russia's UN ambassador Vitaly Churkin said that since the council passed a statement on Syria on August 3, events had seen the West "switch gears and turn into regime-change mode, discouraging dialogue."
Amid the diplomatic wrangling, the death toll continued to mount on Tuesday, when at least 23 civilians were killed, according to activists.
"Seven security force members were killed in an ambush by deserters on a convoy patrolling the Idlib-Bab al-Hawa road in response to the martyrdom of 11 civilians this morning," the Observatory said.
The 11 died when they were attacked by security forces and pro-regime Shabiha militiamen in two villages in northwestern Idlib province, it said earlier.
Eight others were later killed and 19 wounded in a separate incident in Kafr Yahmul, also in Idlib province, when troops fired on crowds attending funerals, according to the Observatory.
Syrian opposition sources based in Turkey said Syrian security forces shot dead a Saudi-Turkish citizen, Mohammed Munir Dolar, as he was travelling with his wife in his vehicle in Kafr Yahmul.
The sources, who requested anonymity, said Dolar was not attending any anti-government demonstration, and it was not immediately clear if his death was among those mentioned in other reports.
State-run SANA news agency said border guards shot dead two "terrorist" infiltrators who were attempting to enter Syria from Turkey.
A Turkish diplomat denied Ankara was allowing attacks to be carried out on Syrian forces from its territory.
Colonel Riyadh al-Asaad, who heads the Free Syrian Army, is based in a Turkish border camp and, unlike some other dissidents, has called for foreign air strikes.
In restive Homs province, meanwhile, security forces shot dead four civilians including a 60-year-old man, activists said, as a blast tore through a gas pipeline near Rastan, according to SANA, which blamed "terrorists."
EU foreign affairs chief Catherine Ashton lamented that two Syrians who are among five Arab Spring activists to win this year's Sakharov prize for freedom of thought would not be able to receive their awards in person at Wednesday's ceremony.
"For obvious reasons they could not come to Strasbourg," she told the European Parliament, referring to lawyer Razan Zeitouneh and cartoonist Ali Farzat.