Syrian president rejects opposition ceasefire offer as his army tightens the noose on rebel-held part of the key city.

Syrian President Bashar al-Assad said a victory for his army in the second city of Aleppo would be a “huge step” towards ending the country’s devastating five-year civil war.

Defeating rebels in Aleppo, however, would not put an end to Syria’s conflict, Assad said in an interview with Syrian daily Al-Watan to be published on Thursday, an early copy of which was seen by AFP news agency.

“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,” Assad said. “But it will be a huge step towards this end.”

Since it began in March 2011, the war in Syria has killed hundreds of thousands of people, made more than half of Syrians homeless, and created the world’s worst refugee crisis.

Government forces scored an important victory on Wednesday when the rebels retreated from the Old City, the historic heart of Aleppo.

They extended their advances later in the day, seizing the Bab al-Nayrab, Al-Maadi and Salhin neighbourhoods, according to state media.

More neighbourhoods were expected to fall soon, but rebels were fighting ferociously.

The Syrian Civil Defence, a first responder group also known as the White Helmets, said air strikes and shelling on Wednesday killed 61 people in what’s left of the rebel-held east of the city.

Syria state television reported late on Wednesday that rebel shelling killed 14 civilians and wounded 70 others, some critically, targeting government-held districts in west Aleppo.

READ MORE: Syria’s war – What went wrong in east Aleppo?

In a blistering, three-week offensive, Syrian forces have seized about 80 percent of east Aleppo, a stronghold for rebel groups since 2012.

Increasingly cornered in a pocket of territory in the city’s southeast, opposition factions on Wednesday called for an “immediate five-day humanitarian ceasefire”.

When asked about the possibility of a truce in Aleppo, Assad said: “It’s practically non-existent, of course.”

Assad told Al-Watan: “The Americans, in particular, are insisting on demanding a truce, because their terrorist agents are now in a difficult situation.”

He said a rebel loss in Aleppo “will mean the transformation of the course of the war across Syria”.

Russian Foreign Minister Sergey Lavrov met US Secretary of State John Kerry in Hamburg late on Wednesday.

“They met for around 45 minutes in the German city of Hamburg where they discussed not only the humanitarian crisis unfolding in east Aleppo, or at least what’s left of east Aleppo, they’re also discussing a deal which would see rebels being able to exit the area,” Al Jazeera’s Imtiaz Tyab said, reporting from Gaziantep along the Turkey-Syria border.

An American official confirmed that the two diplomats discussed the potential safe passage for rebels out of east Aleppo.

An official with an Aleppo-based rebel group, who declined to be named, told Reuters news agency: “The Russians want the fighters out and they [the Americans] are ready to coordinate over that.”

READ MORE: Government forces push into Aleppo’s Old City

While rebels say they could fend off the offensive for some time to come, the fighting is complicated by tens of thousands of fearful civilians trapped in the rebel-held east, many related to the fighters, the official said.

“The civilian burden is very heavy, in a small area.”

As winter sets in, siege conditions are increasingly desperate, exacerbated by increasing numbers of displaced residents and food and water shortages.

A UN official said about 31,500 people from east Aleppo have been displaced around the entire city over the past week, with hundreds more seen on the move on Wednesday.

With hospitals, clinics, water and food cut off, UN chief Ban Ki-moon called the situation was “heart-breaking”.

Sonia Khush, Save the Children Syria director, said tens of thousands of children in Aleppo have become “sitting targets”.

“It defies belief that after nearly six years of suffering through this war, the international community is still willing to stand by as civilians are bombed with seeming impunity,” she added.