Heavy shelling from missile launchers also hit the Damascus suburb of Mesraba during the speech, the Local Coordination Committees of Syria said.
The opposition group reported that at least 101 people were killed in violence across the country on Sunday.
The president's address, carried live on state-run TV, was al-Assad's first since June. Since then, tens of thousands of Syrians have been killed, and the country appears no closer to a resolution.
During his last publicized speech in June, al-Assad called for unity.
"We are in a state of real war, in every aspect of the words. And when we're in a state of war, all of our politics has to be concentrated on winning this war," al-Assad said at the time.
But during the seven months since, reports from inside Syria suggest rebels are gaining ground.
The battles between al-Assad's forces and rebels are raging closer to the president's doorstep, with some of the fiercest fighting taking place near Damascus.
More than 60,000 people have been killed in the Syrian civil war, according to the United Nations. The crisis, which started in March 2011, began when peaceful anti-government protests led to a fierce crackdown by the government and spiraled into and armed uprising and civil war.
CNN cannot independently confirm reports of daily violence inside Syria, because the government has restricted access by journalists.
In an open letter Friday, Ahmed Moaz al-Khatib, head of the National Coalition of Syrian Revolutionary and Opposition Forces, implored the U.N. Security Council and world leaders to take action.
"Our people are subjected to genocide, and our country is being destroyed as the international silence is only encouraging the regime to commit more crimes against humanity," he wrote. "Halting massacres in Syria is an international obligation everyone should bear responsibility for."