Outrage grew on Sunday after Russia and China blocked a UN Security Council resolution condemning Syria for its crackdown on protests, with the opposition saying it handed the regime a "licence to kill."
The rare double veto drew international condemnation, with US Secretary of State Hillary Clinton calling it a "travesty" and vowing to push for new sanctions on Syria.
And France said Europe will strengthen sanctions on Damascus.
"Europe will again harden sanctions imposed on the Syrian regime. We will try to increase this international pressure," French Foreign Minister Alain Juppe said.
He also said France would "help the Syrian opposition to structure and organise itself."
Russia defended its veto on Saturday, saying Western powers had refused to reach a consensus.
"The authors of the draft Syria resolution, unfortunately, did not want to undertake an extra effort and come to a consensus," Deputy Foreign Minister Gennady Gatilov wrote on Twitter.
The veto came hours after the opposition Syrian National Council (SNC) reported a "massacre" overnight Friday in the central flashpoint city of Homs where more than 230 civilians were killed during an assault by regime forces.
On Sunday, activists reported more shelling in the city said 56 people were killed across Syria, half of them civilians, with most of the dead in Homs province.
The death toll rose to at least 104 people reported killed over the weekend -- one of the bloodiest since the uprising against President Bashar al-Assad's regime erupted almost 11 months ago.
Opposition groups say at least 6,000 people have now been killed in Syria.
The second UN double veto in four months fuelled angry reactions from Washington and fears among Syrian activists of a new surge of violence that would once again target Homs.
"We have to increase diplomatic pressure on the Assad regime and work to convince those people around President Assad that he must go and that there has to be a recognition of that and a new start," Clinton said.
"We will work to seek regional and national sanctions against Syria and strengthen the ones we have," she said, stressing the need "to dry up the sources of funding and the arms shipments that are keeping the regime's war machine going."
Russia's Foreign Minister Sergei Lavrov and Foreign Intelligence Service chief Mikhail Fradkov are preparing to visit Damascus on Tuesday, as reports said the mission could try to push Assad to quit.
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"Russia strongly intends to achieve a rapid stabilisation of the situation in Syria through the rapid implementation of much-needed democratic reforms," the Russian foreign ministry said.
The state RIA Novosti news agency ran an analysis quoting Russian experts as saying Lavrov's visit would be aimed at persuading Assad to step down.
The SNC voiced dismay over the UN veto.
"The SNC holds Russia and China accountable for the escalation of killings and genocide, and considers this irresponsible step a licence for the Syrian regime to kill," it said in a statement.
In Libya, crowds of Syrians chanting anti-Russian slogans entered Moscow's Tripoli embassy and replaced the Russian flag with the new Syrian flag in protest while hundreds protested outside the Russian embassy in Beirut.
And Turkish police fired tear gas to disperse protesters seeking to storm the Syrian consulate in Istanbul.
Iran, however, welcomed the veto on the resolution condemning its ally Syria and accused the Security Council of attempting to interfere in the country's internal affairs
"The Security Council has become a tool for the West's bullying ... of other nations, and this time Russia and China stood up against it," said Iran's Foreign Minister Ali Akbar Salehi.
Assad's troops shelled Homs overnight Friday, killing at least 260 civilians, the SNC said, while the Syrian Observatory for Human Rights said about 100 women and children were among its toll of 237 dead.
The tolls could not be independently confirmed. Damascus denied responsibility, blaming the deaths on rebels seeking to swing the UN vote.
The UN resolution -- approved by 13 of the 15-member Security Council -- was proposed by European and Arab nations to give strong backing to an Arab League plan to end the crackdown.
On Sunday, League chief Nabil al-Arabi said the bloc would press on with mediation efforts to find a political solution and avoid foreign intervention in Syria.
Syrian government mouthpiece Tishrin called the veto "a catalyst" and said it would help accelerate reforms in the country.
Tunisia urged other Arab nations to follow its lead after it said on Saturday it was expelling Syria's ambassador and withdrawing its recognition of the Assad government.
The Syrian Observatory said at least 56 civilians, including five children, and 28 regular army troops were killed on Sunday, a day after 48 people were reported dead.