Russia and China have vetoed a UN Security Council resolution proposing further sanctions on Syria, prompting an angry Western response.
The UK, US and France said the UN had failed the people of Syria.
Syrian troops have been mobilised to oust rebels from parts of Damascus, after a bomb killed three senior figures in the defence establishment.
State TV has broadcast the first images of President Assad since the attack, standing with the new defence minister.
The footage appeared to show Gen Fahd Jassim al-Furayj, chief of staff of the armed forces, being sworn into his new post. It was not clear where the meeting had taken place.
Syrian forces have deployed tanks, artillery and helicopters in parts of the capital and clashes have been reported south-west and north-east of the city.
Meanwhile, the rebels are reported to have captured a number of border posts.
Sources told a BBC correspondent on the Turkish-Syrian border that the Free Syrian Army had taken the Sarmada and Bab al-Hawa crossings. However, they were later said to have withdrawn from Bab al-Hawa.
On Syria's eastern border, Iraqi officials told AFP news agency that rebels had taken over the Abu Kamal crossing between the two countries.
Russia and China have used their vetoes twice before over Syria and UK Foreign Secretary William Hague condemned their latest action as "inexcusable and indefensible".
"They have turned their back on the people of Syria in their darkest hour," he said. The UK's ambassador to the UN, Mark Lyall Grant, said he was appalled.
Under the Western-backed plan, the Damascus government would have been threatened with non-military sanctions under Chapter Seven of the UN Charter if it failed to move troops and heavy weapons from populated areas.
It was the use of Chapter Seven that stirred Moscow's objections. It opened the path to "external military involvement in Syrian domestic affairs", Russia's UN ambassador Vitaly Churkin argued.
But US ambassador Susan Rice said that any suggestion of military force was "paranoid if not disingenuous".
The French envoy accused Russia of seeking to gain time for the Syrian regime while the US said it planned to intensify its work outside the Security Council.
With sporadic battles breaking out for control of Damascus, international envoy Kofi Annan has pushed the international community to take urgent and decisive action.
The Security Council still has to decide whether to renew the mandate of a UN mission in Syria, due to end on Friday. The UK is said to be revising the text of the vetoed resolution proposing an extension for a "final 30 days".
The BBC's Jim Muir in Lebanon says the 300 UN observers have found themselves completely sidelined by the violence in Syria. Whether or not the mission is extended, their commander Gen Robert Mood has decided to leave anyway, our correspondent says.
The bombing at Syria's national security headquarters claimed the lives of three high-profile figures in President Assad's defence establishment
- Defence Minister and ex-chief of staff Gen Daoud Rajiha
- Deputy Defence Minister Assef Shawkat, married to Mr Assad's sister Bushra
- Assistant to the vice-president and head of crisis management office Gen Hassan Turkomani
- Two other senior officials - interior minister Mohammad Ibrahim al-Shaar and National Security Bureau chief Hisham Ikhtiar- were wounded
Rebel groups said the bomb had been planted the day before the meeting at national security headquarters where it was detonated. They predicted the government's imminent fall.
After the attack the government vowed to root out ruthlessly what it described as armed terrorists backed by outside powers.
Security forces launched operations in many areas which have seen clashes in recent days, killing many "terrorists".
State media said a rebel command centre had been discovered at Midan. According to activists, 60 people were killed on Wednesday when a helicopter gunship attacked a funeral procession south of the capital.
Tanks and armoured vehicles were reported in Qaboun, close to the city centre on Thursday.
There were heavy casualties, activists said, as a result of an army bombardment of Zamalka in the eastern outskirts of Damascus.
But the rebels are said to be on the offensive too, warning state TV and radio to evacuate staff before its headquarters comes under attack.