A senior Russian official says Moscow and the US are close to reaching an understanding on the situation in the besieged Syrian city of Aleppo.

Russian Deputy Foreign Minister Sergei Ryabkov said Thursday that the two countries had exchanged documents regarding the crisis over the past several days, but he was circumspect about the prospects.

“We are close to reaching an understanding, but I want to warn against high expectations,” Ryabkov said.

The Kremlin said on Wednesday that a potential US-Russia deal to allow Syrian militants to safely leave the besieged city was still on the agenda.

Russian Foreign Minister Sergei Lavrov was scheduled to meet his American counterpart John Kerry in Hamburg, Germany, later on Thursday.

The two men on Wednesday discussed the situation in Aleppo, including the delivery of humanitarian aid to civilians, according to US State Department spokesman John Kirby.

​Syria’s largest city has been the scene of fierce clashes between government forces and foreign-backed militants.

With foreign-backed militants on the verge of total rout, the US and its allies have been urging Russia to pressure the Syrian government into a ceasefire.

Syrian troops and their allies have managed to retake more than two-thirds of the territory that used to be under the control of the militants.

In an interview with al-Watan newspaper expected to be published on Thursday, Syrian President Bashar al-Assad said Aleppo was the “last hope” of militants and their supporters after their failure in the battles of Damascus and Homs.

The Syrian president said the militants' defeat in Aleppo would fully change the course of battle in Syria.

On Thursday, as the army advances continued, the International Committee of the Red Cross (ICRC) said nearly 150 civilians, most disabled or in need of medical care, were evacuated overnight from Dar Al-Safaa hospital in Aleppo's recently-liberated Old City.

Marianne Gasser, the head of the ICRC in Syria, said the patients and civilians had been trapped in the area for days because of heavy clashes nearby and as the front line kept drawing closer.

The ICRC said the evacuation was conducted jointly with the Syrian Arab Red Crescent, during which 118 patients were taken to three hospitals in the west of Aleppo and 30 people were transferred to shelters, also in the west which is under the government control.

Syrian government forces on Tuesday seized control of all parts of the Old City in their operation to flush out Takfiri militants from the strategic northwestern city.