The Syrian leader made the threat in his first address to a newly-installed parliament in Damascus, calling into question his commitment to a UN-led peace process and a truce between government and opposition forces.
"We have no choice but victory," he said, to applause from a parliament elected under civil war conditions in a vote that Washington and Assad's other international critics have not recognized as legitimate.
US State Department spokesman Mark Toner said the belligerent speech was unsurprising and dubbed it "vintage Assad," adding that Washington would call on Russia, its co-chair of the International Syria Support Group (ISSG), to restrain its ally.
"We still believe that Russia and Iran can at least appeal to those in the regime who still have influence on him to refrain from letting this political process, this cessation of hostilities, fall completely apart," Toner said.
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"Again, there is nothing surprising in what he said today but, you know, it was discouraging."
President Barack Obama's spokesman Josh Earnest said Assad's determination to cling to power "only exacerbates the chaos and turmoil" and said Russia's President Vladimir Putin has the power to change his calculus.
"President Putin made a commitment to use that influence to get the Assad regime to abide by the cessation of hostilities," he said.
The ISSG, a 21-nation contact group that includes Assad foes like Saudi Arabia and friends like Iran as well as Washington and Moscow, supported a UN-led process to end Syria's five-year civil war through a negotiated deal.
The outline of a peace plan -- including a "political transition" away from Assad's rule -- has been endorsed by the UN Security Council, but Assad has thus far refused to accept calls for him to step down.