The presidential advisor said the Turkish army, which entered parts of Idlib, will be "forced" to leave Syria.
On Friday, the Syrian army agreed to observe a cease-fire in Idlib, the last major rebel stronghold in the country, as of Saturday morning.
The Syrian army said it reserves the right to respond to any violation by the al-Qaida-linked Nusra Front, the backbone of the Hayat Tahrir al-Sham (HTS), which is the most powerful rebel group in Idlib.
Hours ahead of the official Syrian announcement, Russia's Defence Ministry declared the cease-fire, noting that it is a "unilateral" move to stabilize the situation in Idlib. It urged the rebels to abandon armed provocations and join the peace process.
This is the second truce announced in Idlib this month. On Aug. 1, a Russian and Turkish-backed cease-fire was reached but it quickly collapsed.
Since then, battles flared and the Syrian government forces were able to make notable gains, capturing key areas in the southern countryside of Idlib and the adjacent northern countryside of Hama province.
The new cease-fire aims at halting the fighting in Idlib between the Syrian army and the al-Qaida-linked groups.
The Syrian Observatory for Human Rights said that cautious calm prevailed Idlib on Saturday. However, the Britain-based watchdog group said that the Syrian army fired tens of shells on rebel positions on Sunday.
The countryside of Hama and the adjacent Idlib province are included in the de-escalation zone established by Russia and Turkey last September.
Under the deal, Turkish observation points were set up in some areas in Idlib and Hama. However, the deal failed to materialize as the Nusra Front refused to withdraw and fighting continued.