Bashar Ja'afari, also said his team was pushing for an expanded government as the solution to the war - an idea rejected by the opposition fighting for five years to topple Assad.
Ja'afari was reiterating the Syrian government's position as spelt out last month ahead of the latest round of talks, indicating no shift on the part of Damascus.
"In Geneva we have one mandate only to arrive at an expanded national government only, this is our mandate ... this is the goal we strive to achieve in the Geneva peace talks," Ja'afari said in comments broadcast overnight. He added that these views were relayed to UN Syria mediator Staffan de Mistura.
Ja'afari also said Assad's fate could never be raised in peace talks nor was it a matter that any UN-backed political process could deliberate.
"This matter (the presidency) does not fall under the jurisdiction of Geneva ... this is a Syrian-Syrian affair, Security Council or no Security Council," he said, according to Reuters.
The Western-backed Syrian mainstream opposition decided on Monday to take a pause in peace talks. It claimed Damascus was not serious about moving towards a UN-backed political process they say would bring a transitional governing body with full executive powers without Assad.
A UN Security Council resolution in December called for the establishment of "credible, inclusive and non-sectarian governance", a new constitution, and free and fair elections within 18 months.
Ja'afari also said any ideas such as those floated recently by de Mistura that sought to bridge the gap between the two sides should not touch existing state institutions or the army.
"We won't allow any constitutional vacuum to take place. What does that mean? It means the army stays as it is and state institutions continue to function," he added.
The opposition says restructuring the army and security apparatus is an essential step towards establishing a democratic Syria.
Ja'afari accused the Western-backed opposition of seeking to bring about a collapse of the country and replicate the chaos seen in Iraq and Libya after Western military intervention brought down long severing authoritarian rulers.
"They want to repeat the experience of Libya and Iraq ... and turn Syria into a failed state," he said.