It said at least 260 civilians were killed in the onslaught. The Syrian Observatory for Human Rights said about 100 women and children were among the 237 dead in its toll. Both said hundreds more were wounded.
The Assad regime "committed one of the most horrific massacres since the beginning of the uprising in Syria," the SNC said. Opposition groups say more than 6,000 people have now been killed in the country since last March.
Dozens of bodies and scenes of chaos could be seen in video images shown by the Al-Jazeera and Al-Arabiya television channels.
Church bells rang out and Muslim prayers were recited in Homs mosques for those killed, activists said. Thousands took part in funeral processions across the city.
AFP was not able to verify the authenticity of videos or the tolls because of restrictions on reporting in Syria. But US President Barack Obama denounced the "unspeakable assault" and demanded that Assad step down.
"Assad must halt his campaign of killing and crimes against his own people now. He must step aside and allow a democratic transition to proceed immediately," Obama said in a statement.
The Syrian government denied responsibility for the deaths, blaming them on opposition rebels seeking to influence Security Council debate on Syria. But Russia and China used their diplomatic muscle for the second time in four months to block a resolution condemning the violence.
The other 13 countries in the 15-member council voted for the resolution, proposed by European and Arab nations to give strong backing to an Arab League plan to end the crackdown.
Russia and China "remain steadfast in their willingness to sell out the Syrian people and shield a craven tyrant," US ambassador Susan Rice told the council.
In a separate message on Twitter, Rice wrote: "Disgusted that Russia and China prevented the UN Security Council from fulfilling its sole purpose."
Britain is "appalled" at the veto, said its UN ambassador Mark Lyall Grant, while French President Nicolas Sarkozy "strongly deplores" the veto by Russia and China, his office said.
The Arab League meanwhile renewed its call for Syria to end the crackdown. It said "the escalation of violence has put the Syrian crisis on a dangerous new curve which will lead to an aggravation of the situation and an increase in deaths."
But Russia's UN envoy Vitaly Churkin defiantly rejected attacks from the European and Arab nations that proposed the resolution, which has been negotiated for several weeks.
Churkin justified the veto by saying the proposed resolution "sent an unbalanced signal to the Syrian parties."
His Chinese counterpart Li Baodong said pushing through such "a vote when parties are still seriously divided... will not help maintain the unity and authority of the Security Council, or help resolve the issue."
Western envoys said they had bent over backwards to change the text after Russia had balked at any resolution that could be used to justify foreign military intervention, called for Assad to quit or imposed an arms embargo on Syria.
US Secretary of State Hillary Clinton said she had tried to negotiate with Russian Foreign Minister Sergei Lavrov on the sidelines of the Munich Security Conference in Germany.
But the resolution's backers said they decided to end negotiations and call for a vote after Russia demanded new changes early Saturday.
Russia -- for whom Syria is its last remaining major ally in the Middle East -- announced that Lavrov and intelligence chief Mikhail Fradkov would travel to Damascus on Tuesday to press Assad to discuss a political solution.
As news of the Homs killing spread, protesters stormed Syrian embassies in Athens, Berlin, Cairo, Kuwait and London. Tunisia announced it was expelling Syria's ambassador and withdrawing its recognition of the Assad government.
The Homs attack came on the 30th anniversary of a massacre by Assad's father Hafez in the city of Hama in which tens of thousands died.