As violence flared in other parts of the country yesterday, Turkey said it was to ask Nato to station Patriot missiles along its border with Syria to guard against violence spilling on to its territory.
Syria's war, which has destabilised neighbouring Lebanon and raised the spectre of wider Middle East turbulence, poses one of the greatest foreign policy challenges for US President Barack Obama as he starts his second term.
Damascus residents said heavy-calibre shells apparently aimed at the palace hit the nearby residential Mezze 86 district that is home to members of Mr Assad's Alawite sect. State-run media said at least three people were killed and seven wounded in what it described as a terrorist attack.
"Ambulances are heading to the area and the shabbiha [pro-Assad militiamen] are firing automatic rifles madly in the air," said a housewife who asked not to be named.
Rebels have focused efforts on high-profile attacks against sym-bols of President Assad's rule, such as his palace. A July bomb that killed four of Mr Assad's top lieutenants was shortly followed by a rebel advance into Damascus.
Fighters in the mainly Sunni Muslim opposition have stepped up attacks in the capital this week, setting off bombs in at least two areas populated by Alawites and assassinating two figures seen as close to the the President's administration.
The violence has highlighted the sectarian dimension of a civil war that is deepening the rift between Sunni and Shi'ite Muslims in the region – Mr Assad's Alawite sect is an offshoot of Shi'ite Islam.
An Islamist rebel unit said it targeted but missed the palace, a compound mainly used for official functions which sits on a hill overlooking the city. It was not possible to verify whether the President was staying there at the time. He has several residences across the city.
"This operation came in response to the massacres committed in our beloved city," said the Lions of Islam rebel group. They said they also attacked a military airport and an intelligence facility in the capital, but there was no independent confirmation of those reports.
State media said a judge, Abad Nadwa, was killed in Damascus yesterday by a bomb placed under his car. The brother of the speaker of the Syrian parliament was killed in Damascus on Tuesday.
International and regional rivalries have complicated efforts to mediate any resolution to the conflict – Russia and China have vetoed three UN Security Council resolutions that would have put Mr Assad under pressure.
The United States and other Western powers say a resolution to the conflict has also been frustrated by divisions and in-fighting between Syrian opposition groups.
Prime Minister David Cameron visited a Syrian refugee camp in Jordan yesterday and said efforts so far to halt the bloodshed had been fruitless.
Mr Cameron, who said on Tuesday that offering Mr Assad immunity from prosecution could be a way of persuading him to leave power, said the President would have to face justice.
"I would like to see President Assad face full international justice for the appalling crimes he has meted out on his people," he said.