Assad's statement comes days ahead of scheduled Moscow talks between Russian President Vladimir Putin and a Syrian delegation on the possible relaunch of peace talks with the opposition.
"The defeat of terrorism... requires... applying real pressure on those implicated in financing, arming and facilitating the actions of the terrorists," Assad told the Russian parliamentary delegation, state news agency SANA reported.
Since the outbreak of a 2011 pro-democracy revolt in Syria, Assad has blamed all violence there on "terrorists".
He has also accused Western countries, Turkey, Qatar and Saudi Arabia of backing them.
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The revolt began as a peaceful uprising, but later morphed into an armed insurgency after Assad launched a major crackdown on dissent.
Late last year, the radical Islamic State group (IS) emerged in the Syrian conflict, and has since committed some of the war's worst abuses.
A US-led coalition began a campaign of air strikes against IS positions in Syria in September.
Moscow has been a staunch ally of Assad's regime throughout Syria's civil war, and has repeatedly thwarted UN action against him.
SANA said Assad told the parliamentary delegation he is grateful for Moscow's continued support for his regime.