Few of the 5,000 protesters camped in the so-called red-zone heeded the ultimatum to leave the area on Monday afternoon.
The protesters insist that government troops must lift their blockade of the red-shirt camp before any negotiations.
In a statement, Ms Pillay said: "I urge leaders to set aside pride and politics for the sake of the people of Thailand.
"To prevent further loss of life, I appeal to the protesters to step back from the brink, and the security forces to exercise maximum restraint in line with the instructions given by the government."
The demonstrators, who want Prime Minister Abhisit Vejjajiva to step down, have been occupying large areas of the city since mid-March.
Fires set by the red-shirts have become a symbol of their protest
Sporadic outbreaks of unrest have accompanied their protest, including an attempted crackdown by security forces in April that left 25 people dead.
Violence again broke out last Thursday, and soldiers are now openly using live ammunition; sniper fire has been reported.
RED-SHIRT PROTEST
14 Mar: Red-shirts converge on Bangkok, occupy government district
16 Mar: Protesters splash their own blood at Government House
30 Mar: Talks with government ends in deadlock
3 Apr: Occupy Bangkok shopping district
10 Apr: Troops try to clear protesters; 25 people are killed and hundreds injured
The authorities say they are targeting "terrorists" who have infiltrated the protesters' ranks, but TV footage has shown unarmed protesters being shot in the streets.
While the majority of the red-shirts are conducting their protest peacefully, some have been building barricades of tyres and setting them alight. Witnesses say others are armed with guns.
Late on Monday, the two sides held what is believed to be their first direct talks since the latest unrest broke out.
The government's chief negotiator Korbsak Sabhavasu said red-shirt leader Nattawut Saikuwa had called him and asked for a ceasefire.
But Mr Korbsak told the Associated Press news agency that nothing had been agreed.
On Monday, protests spread outside the capital with a military bus torched in Chiang Mai and demonstrations in two other northern towns.
Many of the protesters are from poor rural areas in the north, where support is still strong for former Prime Minister Thaksin Shinawatra, who was deposed in a 2006 coup.
The protesters say the current government is illegitimate, having come to power in a parliamentary vote after a pro-Thaksin government was forced to step down in December 2008 by a Constitutional Court ruling that it had committed electoral fraud.
Are you in Thailand? What is your reaction to what is happening in the capital right now? What is the best way out of the conflict? Send us your views using the form below.
The BBC may edit your comments and not all emails will be published. Your comments may be published on any BBC media worldwide.
Bookmark with:
What are these?