Meeting a Russian parliamentary delegation as Moscow steps up efforts for a political deal, Assad emphasised the need for greater security.
"The eradication of terrorist organisations will lead to the political solution that Syria and Russia seek and that will satisfy the Syrian people and preserve Syria's sovereignty, independence and territorial integrity," he said, quoted by news agency SANA.
The visit by Russian lawmakers came days after Assad made a surprise trip to Moscow for talks with President Vladimir Putin.
That trip and ramped-up Russian diplomacy have led to speculation that Moscow is pushing for a new political agreement to end the conflict that began with protests against Assad's rule in March 2011.
But the shape of any such deal remains unclear, with Syria's opposition firmly against Moscow leading peace efforts while pursuing an air campaign it launched in support of Assad on September 30.
A Russian lawmaker said today that Assad had expressed a willingness to hold new parliamentary and presidential elections, but only after Syria is "liberated" from Islamic State group jihadists.
"He is ready to conduct elections with the participation of all political forces who want Syria to prosper," the lawmaker Alexander Yushchenko told AFP.
Assad would run again "if the people are not against it," he added.
Russian Foreign Minister Sergei Lavrov has said that Syria needed to begin preparing for new elections.
Syria last held parliamentary polls in May 2012, with the next one planned for 2016.
A presidential election was held in June last year, with Assad re-elected for a seven-year term with 88.7% of the vote.
It was dismissed as a "farce" by the opposition and its supporters, with voting held only in government-controlled areas and millions of the displaced and refugees unable to vote.
It is unclear whether new elections could be held under different circumstances, and Syria's opposition has dismissed holding a vote now as absurd.