His defiant stance, in an exclusive interview with AFP released today, doused hopes of an imminent halt to hostilities, which world powers are pushing to take effect within a week.
Assad said the main aim of a Russian-backed regime offensive in Aleppo province that has prompted tens of thousands of people to flee was to cut the rebels' supply route from Turkey.
He said his government's eventual goal was to retake all of the country, large swathes of which are controlled by rebel forces or the Islamic State (IS) jihadist group.
Assad said it would be possible to "put an end to this problem in less than a year" if opposition supply routes from Turkey, Jordan and Iraq were severed.
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But if not, he said, "the solution will take a long time and will incur a heavy price".
Assad said he saw a risk that Turkey and Saudi Arabia, key backers of the opposition, would intervene militarily in Syria.
World powers agreed today an ambitious plan to cease hostilities in Syria within a week, but doubts soon emerged over its viability, especially because it did not include IS or al-Qaeda's local branch.
Lavrov underlined that "terrorist organisations" such as IS and Al-Qaeda-affiliated Al-Nusra Front "do not fall under the truce, and we and the US-led coalition will keep fighting these structures".
Russia says its more than four-month-old bombing campaign in Syria targets IS and other "terrorists", but critics accuse Moscow of focusing on mainstream rebels.
The Munich deal went further than expected, with Lavrov talking about "direct contacts between the Russian and US military" on the ground, where the powers back opposing sides in the five-year-old conflict.
But after Assad's forces this month nearly encircled Aleppo, Syria's second city, several nations put the onus on Moscow to implement the deal.