Ending the law has been a key demand of the thousands of protesters who have turned out every Friday for the past month. Assad made the announcement as he swore in a new Cabinet, The New York Times reported.
"The blood that was shed in Syria pains us all," he said. "We are sad for every loss. We consider each of them martyrs."
Assad has met the protesters with a combination of carrot and stick -- making concessions such as dissolving the previous Cabinet and granting citizenship to Kurdish families stripped of it in the 1960s -- but security forces have tried to quell protesters with tear gas and bullets.
U.S. Secretary of State Hillary Clinton warned Syria to stop using violence against its own people as thousands took part in anti-government protests, CNN reported. She said the government has failed to address the "legitimate demands" of the Syrian people.
"It is time for the Syrian government to stop repressing their citizens and start responding to their aspirations," Clinton said.
Tens of thousands of demonstrators took part in protests Friday across the country to call for reforms, with some demanding the overthrow of Assad.
The Daily Telegraph said up to 100,000 people gathered outside the capital, Damascus, and another 20,000 demonstrated in Daraa. At times they battled security forces using batons and tear gas.