AMMAN/CILVEGOZU, Turkey - Rebels seized control of sections of Syria's international borders and torched the main police headquarters in the heart of old Damascus, advancing relentlessly after the assassination of Syrian President Bashar Assad's closest lieutenants.The battle for parts of the capital raged into the early hours of Friday, with corpses piled in the streets. In some neighborhoods, residents said there were signs that the government's presence was diminishing."Three patrol cars came to the site and were hit by roadside bombs," said activist Abu Rateb by telephone. "I saw three bodies in one car. Others said dozens of security men and shabbiha (pro-Assad militia) lay dead or wounded along Khaled bin al-Walid street, before ambulances took them away."The next few days will be critical in determining whether Assad's government can recover from the devastating blow of Wednesday's bombing, which wiped out much of Assad's command structure and destroyed his circle's aura of invulnerability.Assad's powerful brother-in-law, his defense minister and a top general were killed in Wednesday's attack. The head of intelligence and the interior minister were wounded.Government forces have responded by blasting at rebels in their own capital with helicopter gunships and artillery stationed in the mountains overlooking it.Assad's failure to appear in public for more than 24 hours - he was finally shown on television on Thursday swearing in a replacement for his slain defense minister - added to the sense of his power evaporating. His whereabouts are not clear.Diplomatic efforts - rapidly overtaken by events on the ground - collapsed in disarray on Thursday when Russia and China vetoed a UN Security Council resolution that would have imposed sanctions unless Syrian authorities halted violence. Washington said the council had "failed utterly."Activists in Damascus said rebels were now in control of the capital's northern Barzeh district, where troops and armored vehicles had pulled out.The army had also pulled out of the towns of Tel and Dumair north of Damascus after taking heavy losses, they said. But they said troops were hitting the western district of Mezzeh with heavy machine-guns and anti-aircraft guns overnight.The reports could not be confirmed. The Syrian government restricts access by international journalists.A resident who toured much of Damascus late on Thursday said he saw signs the government's presence was diminishing, with only sporadic checkpoints and tanks in place in some areas. The Interior Ministry at the main Marjeh Square had a fraction of its usual contingent of guards still in place.Shelling could be heard on the southwestern suburb of Mouadamiyeh from hills overlooking the city where the Fourth Division, commanded by Assad's brother Maher, is based, he said.Syrian television showed the bodies of about 20 men in T-shirts and jeans with weapons lying at their sides, sprawled across a road in the capital's Qaboun district. It described them as terrorists killed in battle.Officials in neighboring Iraq confirmed that Syrian rebels were now in control of the Syrian side of the main Abu Kamal border checkpoint on the Euphrates River highway, one of the major trade routes across the Middle East.Rebels also claimed control of at least two border crossings into Turkey at Bab al-Hawa and Jarablus, in what appeared to have been a coordinated campaign to seize Syria's frontiers.In Damascus, a witness in the central old quarter district of Qanawat said the huge headquarters of the Damascus Province Police was black with smoke and abandoned after being torched and looted in a rebel attack.