But he added that the defeat of rebel groups in the northern city would not end the conflict.
The rebels called for a five-day truce to allow the evacuation of civilians, after withdrawing from their last strongholds in Aleppo's Old City.
But Mr Assad ruled out any ceasefires, as his army continues its offensive.
This is despite new calls for an immediate truce from the US and five Western powers.
In an interview with Syria's al-Watan newspaper, President Assad said: "It's true that Aleppo will be a win for us, but let's be realistic - it won't mean the end of the war in Syria.
"But it will be a huge step towards this end.
"Terrorists are present elsewhere. Even if we finish with Aleppo, we will continue our war against them."
Rebel-held districts in east Aleppo are falling fast, faster than expected. The full story from the battlefield is still emerging.
Areas we've been able to visit are a testament to intense fighting.
The district of Al-Shaar, cleared on Tuesday to enable the army's assault on the Old City, is now in utter ruin. The smoke of battle still hung in the air a day later as did the residue of explosives.
There are also reports of deals to allow rebel fighters to retreat, including from the Old City.
But the most battle hardened fighters, including forces known as the al-Qaeda-linked Nusra Front are vowing to fight on in what remains of the opposition enclave.
The Syrian military, and its Russian and Iranian allies, aren't listening to calls for a truce, or even for humanitarian corridors.
Monday's mortar attack on Russia's field hospital is said to have stiffened Moscow's resolve to finish the battle for Aleppo as soon as possible.
Tens of thousands of civilians are still trapped in rebel-held districts of south-eastern Aleppo.
The rebel groups said those residents were in great danger, adding that they would support any initiative to ease their suffering.
One resident said those districts were now heavily crowded and there were fears that people faced being captured, detained and tortured to death.
"I know people who literally did nothing, they just kept doing nothing for four, five years, they just wanted to stay in their homes and now they are being arrested by the regime," Wissam, a teacher and activist said.
Food supplies are exhausted and there are no functioning hospitals after months of heavy bombardment.
Government forces now control about 75% of eastern Aleppo, held by the rebels for the past four years.
The rebels, who had been left with just a spit of land north-east of the citadel after recent government advances, had abandoned it by Wednesday morning, retreating to territory they still hold further south.
Meanwhile, the US, Britain, Germany, Italy, France and Canada jointly called for an immediate ceasefire "to allow the United Nations to get humanitarian assistance to people in eastern Aleppo".
They also condemned the Syrian government and its main backer Russia for "their obstruction of humanitarian aid", accusing them of targeting hospitals and schools "in an attempt to wear people down".
But fresh talks on Wednesday evening between US Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov ended without a breakthrough on the issue.
Russia and China earlier vetoed a UN Security Council resolution on a week-long ceasefire.
French President Francois Hollande responded by accusing Russia of "systematic obstruction" which "bolsters the regime of Bashar al-Assad in its destructive drive which is harming the defenceless civilian population".
Kremlin spokesman Dmitry Peskov described all the remaining rebels in Aleppo as "terrorists", saying they had united around the jihadist group formerly known as the al-Nusra Front.
Syrian President Bashar al-Assad has said a victory for his army in Aleppo would be a "huge step" towards ending the country's five-year civil war.