Assad also promised "full amnesty" to representatives of the opposition if they lay down their arms and contribute to the resolution of the conflict.
"You just have to lay down your arms, regardless of your desire to take part in the political agenda or not. It does not matter. The most important thing — and this is in the interests of the Syrian people and complies with applicable laws — is that you as a citizen don't have the right to run around with a gun and direct it against people or their property," the Syrian leader said.
According to Assad, rebel groups in Syria violated the truce a few hours after its entry into force, but his army has so far refrained from military actions.
"For our part we will do everything to make it [the truce] work," the Syrian leader said. "We refrain from retaliatory steps to give a chance to the preservation of the truce. We do it, but in the end there is always a limit. It depends on the other side," the politician added.
Earlier, the United States and Russia reached an agreement on a ceasefire between the Syrian government and opposition groups to help end the country's civil war. The Syrian government has confirmed its readiness to halt its military actions in accordance with the Russia-US agreement.
Some opposition forces have been skeptical about the ceasefire, but in general have agreed to adhere to it. The ceasefire took effect on Saturday, but the Syrian authorities claimed that representatives of the opposition continued to violate the truce.