BEIRUT — Syrian rebel fighters, exploiting the psychological momentum gained by their brazen assassination of three top officials, chipped away at the regime’s control Thursday by intensified fighting on various fronts in Damascus and across Syria.

Among other small signs in the continuing deterioration of government rule, the rebels claimed to control a small section of Damascus for the first time after intense street fighting there and also to have captured border crossing points leading to Iraq.

The bombing attack, close to President Bashar Assad’s own residence, called into question the ability of a government that depends on an insular group of loyalists to function effectively as it battles a strengthening opposition. In a move to dispel any rumors that he had been injured or fled the capital, Assad appeared on state television Thursday swearing in a new defense minister.

Opposition activists reported battles between the army and opposition forces in the southern district of Damascus and in the northern suburb of Qaboun, with residents who were not trapped by fighting fleeing many areas.

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The Syrian Observatory for Human Rights, based in Britain, said the government assault had intensified, with more helicopters firing rockets that were igniting and destroying houses in Qaboun.

It said that snipers were deployed around the exits of the neighborhood and that water and electricity had been cut off with numerous families trapped and no one able to
remove the dead from the rubble.

The outlook for a peaceful outcome to the conflict darkened further Thursday, when Russia and China vetoed a Britain-sponsored resolution at the UN Security Council that would have penalized Assad’s government with sanctions for the first time for failing to implement the six-point peace plan negotiated by Kofi Annan, the special Syria envoy.

The double veto also called into question the viability of a 300-member UN mission sent to Syria to monitor the peace plan. Its mandate expires Friday.

Susan E. Rice, the US ambassador, denounced the vetoes. “We have missed yet another critical opportunity to work together,’’ she told the council. Rice called it a ‘‘dark day.’’

In a second statement in two days, the Syrian military said Thursday that the bombing had left it more determined to ‘‘clear the homeland of the armed terrorist groups’’ — the term it uses for the insurgents seeking Assad’s ouster.

Iraqi government officials said Thursday evening that Syrian rebels had wrested control of all four border checkpoints between Iraq and Syria, and that additional Iraqi forces were being sent to the border.

One top government official, who spoke on condition of anonymity, said that the border crossings, in Anbar and Nineveh provinces, were closed and that Iraqi border forces had witnessed the executions of several Syrian army soldiers at the hands of the Free Syrian Army rebels and the raising of the rebels’ flag.

The acting minister of interior, Adnan al-Assadi, was quoted by Agence France-Presse as saying that Iraqi forces had witnessed the executions of 22 Syrian soldiers.

One activist reached in Damascus, using only the name Omar, said the government had been asking residents of Tadamon and parts of Yarmouk, the capital’s southern neighborhoods, to leave their homes. That is usually a sign that government forces are on the verge of a violent attack.

Residents of Mezze and Kafr Sousseh, western neighborhoods even closer to the center of the city, fled unprompted because of the intensity of the shelling there, activists said.

Another activist, Ali Salem, said residents of some five districts of the southern districts of the capital had been warned to leave and those neighborhoods were largely empty. “They threatened them and gave them 24 hours to leave their homes or they will be shelled,’’ he said.

At least some of the Assad family has left Damascus.

One opposition figure said a person associated with air force intelligence told him that a plane left Mezze military airfield in Damascus on Wednesday afternoon for Latakia carrying Assad’s mother, Anisa Assad, the widow of the former president Hafez Assad; his wife, Asma, and their three children, and other women and children from the family.

It is possible the family is gathering for a ceremony in Qardaha, above Latakia, to bury Assef Shawkat, the most significant of those who died in the attack Wednesday.