Hillary Clinton has called on the United Nations Security Council to make a renewed effort to deal with the conflict in Syria.
The US Secretary of State said the body was “paralysed”.
UK Prime Minister David Cameron has also demanded UN action.
France, Britain and the United States are in favour of taking stronger action against President Bashar al-Assad, but Russia and China are backing the Syrian government.
Earlier on Wednesday, suicide bombers attacked a military HQ in Damascus.
Mrs Clinton said that the Security Council must end the violence and urged the members to “try once again to find a path forward”.
David Cameron also called on the UN to act, telling the annual meeting of the UN General Assembly that recent evidence of crimes against children in Syria is “a terrible stain on the reputation of this United Nations”.
He singled out those countries which “failed to stand up to these atrocities and in some cases aided and abetted Assad’s reign of terror” for particular criticism.
The five permanent members of the council, who all hold vetoes, have so far been unable to agree on a course of action regarding the conflict in Syria, which has claimed some 27,000 lives over the last 18 months.
‘Plume of smoke’
The attack on the Syrian military staff command compound on Wednesday morning killed four military guards, according to Syrian officials.
It happened early in the morning close to one of the city’s busiest areas, Umayyad Square, which is dominated by government buildings.
BBC cameraman Phil Goodwin was in a hotel nearby when the attack struck.
“The first blast shook the entire building I was in and sent a huge plume of smoke in the sky,” he said.
The rebel Free Syrian Army and an Islamist group called Ansar al-Islam both said they carried out the attack.
Phil Goodwin describes the scene in Damascus as CCTV shows the moment of attack
State TV broadcast footage of a minibus slowing before exploding at the HQ.
Gunfire reverberated around the city for hours after the bombings, as rebels fought with soldiers at the compound.
As well as this attack, Ansar al-Islam has also said it was behind another assault on a school on Tuesday it said was being used by security forces and militiamen.
Strategic attack
The BBC’s Rafid Jabboori in Damascus says the target and timing are very significant.
The staff command compound represents the heart of the Syrian army, he says.
And the attack comes days after the Free Syrian Army announced it had moved its command from Turkey to Syria in an apparent attempt to bolster its fight against regime forces.
Security measures were stepped up around the military compound after a rebel attack in July killed several senior security officials, including the defence minister and President Bashar al-Assad’s brother-in-law.
Although the attack is a spectacular coup, the rebels do not seem to have caused high-level military casualties, or to have taken and held ground, the BBC’s Jim Muir in Beirut reports.
And they have diverted attention from terrible carnage elsewhere, including in nearby suburbs, where activists say dozens of people have been summarily executed by regime forces.
The pro-opposition Syrian Observatory for Human Rights says 40 bodies were found in the town of al-Dhiyabiyeh near Damascus and that pro-government militiamen murdered 16 civilians in their homes in Damascus in the early hours of Wednesday.
BBC