Idlib and adjacent rebel territory are home to some three million people, about half of them displaced from other parts of Syria.
Muallem's upbeat speech praised the army and the Syrian people for remaining "defiant" during the war, "fully convinced that this was a battle for their existence".
Pro-Turkey rebels began Sunday withdrawing from areas in northern Syria under a deal brokered by Ankara and Moscow to avert a large-scale military assault on the country's last major opposition stronghold, a monitor said. "All conditions are now present for the voluntary return of refugees to the country they had to leave because of terrorism and the unilateral economic measures that targeted their daily lives and their livelihoods".
The demilitarized zone will be 15 to 20 km (10 to 12 miles) deep, run along the contact line between rebel groups and government troops, and will be patrolled by Turkish and Russian forces.
"We hope that when the agreement is implemented, the Nusra Front and other terrorists will be eradicated, thus eliminating the last remnants of terrorism in Syria", Muallem said.
Russia-backed Assad regime forces have massed around Idlib province in recent weeks, sparking fears of an imminent air and ground attack to retake the opposition bastion.
An offensive by government forces on Idlib - the last remaining rebel stronghold - was averted last week when Russian Federation and Turkey reached a deal to establish a demilitarised zone around the province. Emails seeking comment from the U.S., France and Turkey weren't immediately answered.
He said Damascus would continue "fighting this sacred battle until we purge all Syrian territories" of both terror groups and "any illegal foreign presence".
The United Nations, which backed the Russia-Turkey deal, had warned that an all-out assault on Idlib would trigger a humanitarian catastrophe and possibly one of the worst bloodbaths of Syria's seven-year war.
On the issue of refugees, Moualem said the conditions were fine for them to return, and he blamed the worldwide community for "spreading irrational fears" that prompted refugees to stay away.
The United States, aided by Syrian Kurdish-led fighters, helped rout the Islamic State extremist group from all urban areas in Syria but remains in the country because pockets of IS militants remain.
Muallem blamed the global community for "spreading irrational fears" that prompted refugees to stay away.
"We have called upon the worldwide community and humanitarian organisations to facilitate these returns", he said. "They must realize they will not achieve politically what they failed to achieve by force".