Assad made the remarks in a telephone conversation with Putin on Saturday, a day after four gunmen shot dead 133 people and injured 150 more in the Crocus City Hall in the Moscow Region.
Assad said the terrorist attack in Moscow shows that terrorist operations will not be stopped unless the terrorists are destroyed.
The Syrian president said the Daesh terrorist group is "the cousin of Nazism."
Assad said it is not the first time that Russia has faced terrorism and it has always emerged victorious.
Assad said that “We are confident that Russia will emerge victorious from this terrible experience, and we in Syria are waiting for its victory because we have suffered and continue to suffer from terrorism, and the victory over terrorism and Nazism will compensate for the damage caused.”
President Putin thanked Assad for his expression of sympathy and also thanked him for Syria’s willingness to support Russia in the fight against terrorism.
“When we are united, our goal will be achieved and victory will be won,” Putin noted.
Four gunmen opened fire at the rock concert on Friday before a major fire spread through the theatre, Russian authorities and news agencies said.
In a televised address on Saturday, President Putin said 11 people had been arrested, including the four gunmen who carried out the attack.
"They tried to hide and moved towards Ukraine, where, according to preliminary data, a window was prepared for them on the Ukrainian side to cross the state border," he said.
Putin said that “all the perpetrators, organizers and those who ordered this crime will be justly and inevitably punished.”
“Whoever they are, whoever is guiding them," he added.
"We will identify and punish everyone who stands behind the terrorists, who prepared this atrocity, this strike against Russia, against our people," the Russian leader announced.