"Over the last hour we've received information that the military activities in east Aleppo have stopped," Churkin said, according to a simultaneous translation provided by the United Nations.
"So there's no question about cessation of hostilities, or humanitarian operations. The Syrian government has established control over east Aleppo so now the stage has come for practical humanitarian initiatives."
At the same time, sources inside Aleppo tell CNN a ceasefire and evacuation agreement has been reached in the beleaguered eastern part of the city.
Journalist and resident Karam al-Masri, who is in Aleppo, told CNN Tuesday that residents received cell phone messages from rebel leaders announcing a ceasefire.
Aleppo Media Center posted to its Facebook page on Tuesday that a ceasefire had been announced in Aleppo "in preparation for the evacuation of civilians from besieged areas through safe passages."
The Aleppo ceasefire and evacuation agreement was reached with "Turkish mediation," a commander in the Islamist rebel group Ahrar al-Sham told CNN, adding that civilians will start being evacuated from the eastern area of the city Wednesday morning local time.
An activist in Aleppo told CNN the evacuations will begin at 6 a.m. (11 p.m. Tuesday ET).
The first group of civilians to leave will consist of 70 injured people and family members -- a total of 150 people.
- Russia: Syrian regime establishes control over eastern Aleppo
- Ceasefire, evacuation deal forged
- Turkish mediation led to the deal
- Evacuations will begin Wednesday morning
- UN Security Council meets, aims tough words at Syrian regime
- Forces loyal to Bashar al-Assad killed 82 people on Monday, United Nations says
- In light of reports of executions in Syria, CNN's Impact Your World team has ways viewers/readers can help Syrians. Please visit CNN.com/impact
The Turkish Foreign Affairs Ministry confirmed that talks between rebels in eastern Aleppo and the Russian military led to the ceasefire deal. Under the agreement, civilians and then opposition fighters will evacuate to nearby Idlib, the ministry said.
Turkey said its diplomats had been working on establishing a humanitarian corridor in Aleppo for weeks and that their efforts "increased in recent days."
There has been no confirmation of a cessation of hostilities or an evacuation agreement by Syrian state media.
The UN Security Council held an emergency meeting Tuesday to address the situation. Afterward, Staffan de Mistura, UN special envoy to Syria, said he was informed by the Russian ambassador that an agreement on Aleppo was reached.
But the United Nations still needs to verify the deal, de Mistura said.
"We need to verify that on the ground, that they have reached an agreement with the armed opposition. It is imminent, if not already taking place," he said. "It's not clear to me yet as whether they are allowed to withdraw with their light weapons, which was one of the issues which had been discussed, or without weapons."
De Mistura also reiterated the need for the UN to have access to eastern Aleppo to independently verify what is going on there.
'We have failed the people of Syria'
The developments came as government forces continued their advance on the last rebel-held neighborhoods
in Aleppo in their bid to retake the city, once Syria's commercial and cultural heart.
Earlier, a spokesman for the UN High Commissioner for Human Rights, Rupert Colville, said he had been told that 82 civilians, including women and children, were shot in their homes or on the streets Monday.
The gruesome reports of executions prompted the UN Security Council's emergency meeting Tuesday afternoon at the urging of the United Kingdom and France. Tough words were aimed at Syria and its allies.
"We have collectively failed the people of Syria," said UN Secretary-General Ban Ki-moon.
US Ambassador to the UN Samantha Power excoriated Syria, Russia and Iran for the bloodshed in Aleppo and asked, "Are you truly incapable of shame? and "Is there nothing you will not lie about?
"Your barrel bombs and airstrikes ... it is your noose," she said. "Three member states of the UN contributing to a noose around civilians."
Rebel groups held eastern Aleppo for more than four years after the Arab Spring uprising and a Syrian regime siege on the area had essentially cut it off from the outside world, sparking a humanitarian crisis there.
Thousands were fleeing Monday as bombs continued to fall on the remaining rebel-held areas of the city.
Activists said anyone with links to the rebels who seized control of the enclave in 2012 was being hunted down.
"Every hour, butcheries are carried out," the Syrian Observatory for Human Rights said.
The Syrian government did not comment on the killings in state-run media. CNN has not been able to verify the execution reports.
Aleppo on the brink
Humanitarian volunteers in Aleppo have issued a desperate plea for help and safe passage for the estimated 100,000 civilians and rebels still trapped in the city's east, now a wasteland of carnage and rubble.
Amid the chaos, the self-styled Syria Civil Defense volunteer rescue group -- also known as the White Helmets -- was among groups pleading for safe passage out of Aleppo for their volunteers and civilians.
"The regime has been trying to kill us for five years," the group said on Twitter. "Please don't give them this chance."
"We hear children crying, we hear calls for help, but we just can't do anything."
The Assad regime was already in control of western Aleppo and in just over two weeks has taken most if not all of the east. Seizing the whole of Aleppo would put the government in control of Syria's five major cities, marking a turning point in the war.
A 7-year-old girl who has been tweeting from eastern Aleppo wrote an ominous post Tuesday: "This is my last moment to either live or die."
Another Twitter user -- who goes by the user name "Mr_Alhamdo" and says he is a "teacher, activist and reporter" in the city -- posted a number of tweets bidding farewell to his followers, describing the scene as "doomsday."
"This is a call and might be the last call," he said in one. "Save Aleppo people. Save my daughter and other children."
Some of those left in the last few rebel-held areas had begged the international community to stop the regime's advance.
"Please, go to the embassies and block the way," said Salah Ashkar, an activist in east Aleppo, in a video posted on Twitter.
"Please, don't let them sleep. Do it, do it, do it, do that now. There is no minute to spare. Please, please, stand with Aleppo," he said.
But for others, the regime's military push was cause for celebration. Syrian state-run Ekhbariya TV broadcast people chanting with joy, firing gunshots in the air and blaring car horns.