Talks brokered by Syrian ally Russia and rebel supporting Turkey are supposed to take place in Kazakhstan before the end of January, but last week opposition groups said they had frozen the process in light of continued government strikes across the country.
In comments made to French media published on Monday, Mr Assad said that the nationwide truce had been violated by rebels several times. He also defended the army's push to recapture Wadi Barada, a rebel-held valley near Damascus where the main water supply to the capital has been turned off.
There has been disagreement between the government and the rebels of the umbrella group known as the Free Syrian Army over whether certain factions in Wadi Barada - some with al-Qaeda or other extremist links - are part of the truce.
Asked if he would be willing to step down as president - a demand the rebels have insisted on throughout the conflict - Mr Assad said "yes, but my position is linked to the constitution."
"If [the opposition] want to discuss this point they must discuss the constitution," he said. Any constitutional matters must be put to a referendum and the people would elect any president, he added.
Mr Assad's position in the war has been significantly bolstered following the recapture of the northern city of Aleppo last month, which was the last rebel urban stronghold in the country.
The UN said the relentless Russian-backed bombardment of besieged rebel controlled neighbourhoods, which appeared to target civilian infrastructure such as hospitals and bakeries, could amount to war crimes.
If talks go ahead, it is not yet clear who will represent Syria's opposition groups. No hard date has been set for the negotiations, which are supposed to take place in Astana.
Several rounds of talks brokered by the UN have so far failed to bring peace to the almost six-year-long conflict.
The complex civil war has left more than 400,000 people dead and displaced half the Syrian population from their homes.
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