Despite pleas from increasingly cornered opposition fighters, Western countries and the UN, Assad also rejected talk of a ceasefire in Aleppo.
Repeated diplomatic efforts this week to end the fighting have stalled, with US Secretary of State John Kerry and Russian counterpart Sergei Lavrov failing to make a breakthrough in their latest talks.
In a wide-ranging interview with Syrian daily Al-Watan, Assad was confident of victory though he admitted retaking the city would not end the country's conflict entirely.
"Let's be realistic -- it won't mean the end of the war in Syria," Assad said. "But it will be a huge step towards this end."
Regime forces have retaken about 80 per cent of former rebel territory in Aleppo since launching an all-out offensive three weeks ago to recapture Syria's second city.
After a highly symbolic retreat from Aleppo's Old City, the rebels yesterday called for a five-day ceasefire to allow for the evacuation of thousands of civilians still in opposition-held territory.
But Assad's government has said a truce is only possible after a full rebel withdrawal from Aleppo, and opposition fighters have rejected any talk of abandoning the city.
Assad's forces, backed by foreign fighters from Iran and Lebanon's Shiite Hezbollah movement, were continuing to advance, the Syrian Observatory for Human Rights said.
The Britain-based monitoring group said there was heavy rocket fire on several rebel-held districts and fighting in the Salaheddin and Bustan al-Qasr neighbourhoods.
The assault has prompted a mass exodus of residents, with the Observatory saying at least 80,000 have fled their homes.
Syrian troops and aid groups have been helping to evacuate residents from newly retaken areas of east Aleppo, where civilians lived for months under heavy bombardment and a regime siege.
"These patients and civilians had been trapped in the area for days because of heavy clashes nearby and as the front line kept drawing closer," said ICRC Syria delegation head Marianne Gasser.
"Many of them cannot move and need special attention and care. It must have been terrifying for them," she said.
It was unclear how many civilians remained in rebel-held territory, but there were an estimated 250,000 in east Aleppo prior to the latest offensive.
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