"The gravity of ongoing violations and the brutal attacks against the peaceful protesters in that country demand your continued attention," UN rights chief Navi Pillay told an opening session of the council in Geneva.
More than 2,200 people have died in the Syrian regime's crackdown, Pillay told the meeting that was expected to condemn the bloodshed when it resumes talks on Tuesday.
UN chief Ban Ki-moon also piled on the pressure, saying Assad had failed to keep promises, including one he made during a telephone conversation last week to halt the military crackdown.
"It is troubling that he has not kept his word," Ban told reporters. "Many world leaders have been speaking to him to halt immediately military operations, killing his own people. He should do that."
Assad on Sunday night rejected calls by US President Barack Obama and other world leaders to step down even as the regime of another autocratic Arab ruler, Libyan leader Moamer Kadhafi, was crumbling.
The Geneva meeting was to consider a draft resolution deploring the "indiscriminate attacks" on Syrian demonstrators and seeking an end to the violence, a copy of the text said.
The text seen by AFP also underscores the need to send independent investigators to probe the government's crackdown on protesters as Pillay said that more than 350 people had been reportedly killed since August 1.
There was more bloodshed on Monday as eight people were killed, including four shot dead by security forces who fired on protesters at a rally in Homs as a UN fact-finding team visited the city.
The Syrian Observatory for Human Rights, which reported the killings, said six people were killed in Homs and two in Hama, both in central Syria, and several wounded.
Hundreds of people took to the streets when they heard the UN mission was in town, Observatory chief Rami Abdel Rahman told AFP by telephone, apparently to make their voices heard.
"Four people were killed and several wounded when some shabiha (pro-regime militiamen) and members of the security forces opened fire," he said.
After the protests, Syrian authorities ordered the team to leave Homs "for security reasons", UN deputy spokesman Farhan Haq told reporters in New York. "The mission did not come under fire."
The team, which arrived Saturday for a five-day visit, began its work the next day in Damascus to assess humanitarian needs, officials said. While the team was in the suburb of Douma, protesters rallied against Assad.
A defiant Assad told state television late Sunday he would not heed global demands to quit power no matter the pressure on his regime. "While withholding comment, we tell them that their words are worthless," he said.
Assad, who has insisted his forces are battling "armed gangs" determined to sow chaos in his country and his envoy to Geneva, Faysal Khabbaz Hamoui, warned that Syria was targeted by countries aimed at weakening it.
"Syria has been subjected to and continues to be subjected to an unprecedented misleading campaign carried by a number of countries in order to weaken Syria and to change its political position," said the diplomat.
He also slammed the Human Rights Council's draft resolution, saying that "the language used is ... hateful".
Assad's television appearance Sunday came as Libyan rebels swept through swathes of Tripoli, while the veteran Libyan leader's whereabouts remained a mystery.
Prominent Syrian opposition leader Fayez Sara said developments in Libya would have a "positive impact" on Syria but stressed that "the pulse of the street" was different in Damascus.
Syria's pro-democracy opposition has vowed to bring down Assad's regime without foreign intervention.
Assad signed a decree Monday to SET up a commission -- chaired by the prime minister and comprising a magistrate and two lawyers -- tasked with legalising the political parties which he authorised earlier in August.
But in Sunday's interview he stressed Syria will reform at its own pace.
"When they speak of reforms, Western colonialist countries mean that we must give them everything they want, that we abandon resistance, that we abandon our rights. They shouldn't even dream of it," he said.
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