His comments, published by Al-Akhbar, reportedly came during meetings with Lebanese visitors in Damascus and appeared intended to refute any suggestion that Israeli raids on Syrian targets would halt assistance to the Shiite group Hezbollah in Lebanon.
The newspaper said visitors quoted Assad as expressing "confidence, satisfaction and great gratitude towards Hezbollah."
The organisation is a long-time ally of the Syrian regime and has sent fighters to battle alongside Assad's troops, particularly in the Qusayr district of the central province of Homs.
"We have decided to give them everything," the newspaper quoted him as saying, without elaborating.
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"For the first time we feel that we and they are living in the same situation and they are not just an ally we help with resistance," he said.
"We have decided that we must move forward towards them and turn into a nation of resistance like Hezbollah, for the sake of Syria and future generations."
Assad was quoted as saying Syria could "easily" respond to Israeli air strikes by "firing a few rockets at Israel."
"After the strike, we are convinced that we are fighting the enemy now, we are pursuing its soldiers deployed throughout our country," he said, in apparent reference to rebel forces, which the regime has accused of being allied with Israel.
The Jewish state reportedly carried out two raids last week against military targets inside Syria, killing dozens of military personnel.
Israeli sources said the strikes targeted weapons bound for Hezbollah.
Israel has warned repeatedly that it will not allow Syria to transfer advanced weaponry to the Lebanese group, with which it fought a devastating war in 2006.