"Russia can play a role so that Israel no longer attacks Syria," Assad told Russian journalists yesterday.
"I think Russia can play an important role in this regard."
Russia's foreign ministry yesterday summoned Israel's ambassador over air strikes close to Moscow's forces near the historic Syrian city of Palmyra.
The air strikes on Friday prompted retaliatory Syrian missile launches, in the most serious incident between the two countries since the war began six years ago.
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Assad was quoted in comments translated into Russian that "any military operation in Syria that does not have the consent of the Syrian government is illegal".
"If there are some troops on Syrian soil, it is an invasion," he said, adding that the "protection of our borders is a right and a duty".
Syria's military said it had downed an Israeli plane and hit another as they were carrying out pre-dawn strikes near Palmyra, but the Israeli military denied that any planes had been hit.
Russia and Israel had already set up a "hotline" aimed at avoiding air clashes over Syria, which Moscow said it would like to see work more effectively.
For its part Israel has said that it does not usually inform Moscow ahead of time when it will carry out an air strike.