In a speech Sunday, Assad struck a defiant tone, ignoring international demands to step down and saying he is ready to talk — but only with those "who have not betrayed Syria." He also vowed to continue the battle "as long as there is one terrorist left," a term the government uses for rebels.
The opposition rejected the offer, which also drew harsh international criticism.
The Observatory and other activists also reported heavy fighting Tuesday in suburbs of Damascus, including the Sayda Zeinab district, and shelling of the towns of Beit Saham and Aqraba, both near Damascus airport.
The Observatory also said three shells were fired at the suburb of Jaramana, wounding 9 people.
As fighting rages on, more than one million Syrians are suffering from food shortages but are out of reach of vital aid because of the fighting and government restrictions, according a statement Tuesday by the World Food Program.
The conflict started as peaceful protests against the Assad rule, but it turned into a civil war after a harsh government crackdown. More than 60,000 people have been killed since the uprising began in March 2011.
Surk reported from Beirut.