Rebel fighters also clashed with troops in several neighbourhoods of Aleppo on Friday in what the Britain-based Syrian Observatory for Human Rights said was the fiercest fighting so far in Syria's second city.
At the United Nations, the Security Council voted unanimously to give a "final" 30-day extension to a troubled observer mission that was charged with overseeing a peace plan for Syria but which suspended its operations on June 16 in the face of mounting violence.
Friday's vote followed emergency consultations just hours before the expiry of the 300-strong mission's mandate, after Russia threatened to use its veto powers as a council permanent member for the second time in as many days.
In Syria, state television trumpeted the news of the military's Damascus offensive.
"Our brave army forces have completely cleansed the area of Midan in Damascus of the remaining mercenary terrorists and have re-established security," it said, using the regime term for rebels.
Reporters taken on a regime-organised trip of Midan saw three bodies, empty streets, shuttered shops and buildings pockmarked with bullet holes.
The counter-offensive by the army came after a Wednesday bombing killed four senior members of the regime, including the national security chief, who died on Friday.
General Hisham Ikhtiyar had been wounded along with Interior Minister Mohammed al-Shaar in the National Security headquarters bombing, which was claimed by the Free Syrian Army (FSA).
Defence Minister General Daoud Rajha, President Bashar al-Assad's brother-in-law Assef Shawkat and General Hassan Turkmani, head of the regime's crisis cell on the uprising, were all killed in the explosion.
A state funeral was held for the three in Damascus on Friday ahead of their burials in their native provinces, the official SANA news agency reported, adding that Vice President Faruq al-Shara had attended but not Assad himself.
A security source told AFP the army was now in control of the Damascus neighbourhoods of Midan, Tadamon, Qaboon and Barzeh, while fierce clashes were reported in other districts including Jubar, Mazzeh and Kfar Sousa.
The Observatory also reported intense fighting in several neighbourhoods of Aleppo and said troops opened fire on a large demonstration in the city, Syria's commercial centre.
It said 177 people were killed nationwide, including 119 civilians, at least seven of them children.
The deaths came after 302 people were killed on Thursday, the deadliest day of the uprising so far.
Amnesty International said the rebels too could be held criminally responsible for the deaths of civilians as they took the fight to residential areas of the large cities.
An AFP photographer reported that FSA fighters fought a raging battle with Syrian troops at the Bab al-Hawa border post with Turkey and that some 150 rebels controlled the crossing on Friday.
Three more generals crossed into Turkey, bringing to 24 the number of generals who have defected to Syria's northern neighbour, a foreign ministry diplomat told AFP.
On Thursday, Iraq's deputy interior minister Adnan al-Assadi told AFP that the FSA had seized control of all three crossings along their common border.
At the Albu Kamal border point, an AFP photographer saw a watchtower apparently empty and immigration buildings deserted.
But later in the day, medics and rebel fighters reported heavy shelling by the army of Albu Kamal town.
Residents on the Iraqi side of the border said that relatives in the town were desperately trying to cross but that they were being turned back by Iraqi troops.
Iraqi Prime Minister Nuri al-Maliki called on the United Nations on Friday to intervene to provide safe passage for Iraqis escaping the escalating violence in Syria.
The Iraqi government also warned it would not be able to assist Syrians looking to escape the bloodshed.
At the United Nations, Security Council permanent members Russia and China both voted in favour of a resolution extending the mandate of the UN Supervision Mission in Syria for a "final" 30 days, a day after blocking another text that could have imposed sanctions on the regime.
Thursday's vetoes sparked Western outrage but Russian ambassador Vitaly Churkin had threatened to use Moscow's veto again.
US National Security Adviser Thomas Donilon will head to China on Sunday, in the wake of Beijing and Moscow's veto, and will also visit Japan, the White House announced.
Russia had wanted an unconditional extension of the mission for a renewable 45 days.
Russia and Western members of the Security Council remained divided over whether the resolution means the end of UNSMIS.
The text says the council renews UNSMIS for "a final period of 30 days" and stresses the "increasingly dangerous security situation" in Syria.
But it adds that the council would be willing to look at a further extension if UN Secretary General Ban Ki-moon "reports and the Security Council confirms the cessation of the use of heavy weapons and a reduction in the level of violence sufficient to allow UNSMIS to implement its mandate."
US ambassador Susan Rice said it would be "unlikely" that the violence in Syria would ease enough to allow a continued UN presence.
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The situation on the ground is so fluid, that nobody knows how it develops. Assad's forces are better armed as the rebels. Yet they are exhausted, as they have been deployed from one hotspot to another. The rebels employ the guerilla tactic and play hide-and-seek with the regime forces. They evaporate once government troops appear and return and reclaim the land, once they are gone. It's highly doubtful that Assad will regain full control over Syria again.