"Given there has been no let-up in the conflict since the end of November, we can assume that more than 60,000 people have been killed by the beginning of 2013," Pillay said in a statement.
"The number of casualties is much higher than we expected, and is truly shocking," she added.
Pillay said in December 2011 that the UN was unable to provide precise figures on the number of deaths. Since then, media have been relying on the Syrian Observatory for Human Rights, which put the total on Monday at more than 46,000.
"Although this is the most detailed and wide-ranging analysis of casualty figures so far, this is by no means a definitive figure," Pillay said.
Analysis has shown a steady increase in the average number of documented deaths per month since the beginning of the conflict, growing from around 1,000 in the summer of 2011 to an average of more than 5,000 since July 2012.
The Observatory said a regime air strike in the Eastern Ghuta region of Damascus killed or wounded dozens of people, many of them horribly burned.
"There are 12 bodies that have been found at the scene, including a number of rebels from different local battalions," Observatory director Rami Abdel Rahman told AFP by phone. "It is not yet clear if the gas station was the target."
The Local Coordination Committees, a grassroots network of activists, estimated that at least 50 people were killed and dozens of others wounded.
It said the toll was likely to rise because bodies were still being pulled from the rubble, adding that "it is extremely difficult to count the dead because most of the bodies have been immolated."
A gruesome video posted on YouTube purported to show the aftermath of the attack, with many of the bodies burned.
It was not immediately clear if the bomb blasts caused the storage tanks to explode, but the scene was engulfed in fire, which suggests that was the case.
"MIG warplane strikes on Eastern Ghuta! Dozens of martyrs!" a man in the video shouted out as he and a fellow cameraman raced toward plumes of smoke to survey the damage.
One man stood wailing to God as he held what was left of his friend, a head and a shredded torso with a bloodied shirt still hanging on flaps of skin.
Another man was still atop a motorcycle in the middle of the fire, his body engulfed in flames.
The Observatory gave a toll of 127 people killed nationwide, including 60 civilians. Among the civilians were 12 members of the same family, most of them children, who died in an air raid in a town southwest of Damascus.
Warplanes also attacked insurgent strongholds in and around the capital and regime forces clashed with rebels in the north of the country, mainly around the Taftanaz airbase in Idlib province, the watchdog said.
The state news agency SANA, quoting an unnamed official, said unit guarding the airbase repelled multi-pronged attacks by rebel fighters, and a resident said jihadists were leading the assaults.
The family of US reporter James Foley, which had earlier asked media not to report his abduction in the hope that a low profile would assist in efforts to free him, broke their silence on Wednesday to reveal his plight.
"We want Jim to come safely home, or at least we need to speak with him to know he's okay," said his father, John Foley. Addressing the captors he said: "To the people who have Jim, please contact us so we can work together toward his release."
Foley, 39, an experienced reporter who has covered other conflicts, was seized by armed men in the town of Taftanaz province on November 22, along with a driver and a translator who were later released, according to witnesses.
No group has claimed responsibility for the abduction.