Aleppo, a constant battlefield in the long-running Syrian civil war, has been divided between opposition control in the east and government control in the west since 2012.
Russian President Vladimir Putin will seal a deal with Indian Prime Minister Narendra Modi during an upcoming visit to deliver Moscow's most advanced air defence system, the Kremlin said Thursday.
The US and France termed the assaults "war crimes", and said Syria and Russian Federation were responsible.
Up to 300,000 people are still believed to be trapped in the besieged parts of eastern Aleppo.
According to The Aleppo Media Centre, a group of opposition activists in the city, the overnight air strikes killed and wounded a number of people, with some buried under the debris.
Lavrov has said a major reason the September 9 cease-fire agreement that he reached with Kerry failed was the inability of the USA and other countries trying to oust Syrian President Bashar Assad to separate the moderate opposition groups they support from the former al-Qaida affiliate once known as the Nusra Front.
"This is the importance of Aleppo now", Assad said.
At Saturday's smaller meeting, Churkin said, "I think it will be very important to see: Are they prepared to really work for a cessation of hostilities?"
Syria has been plunged into some of the worst violence of the five-year civil war after a hard-won truce collapsed as government forces backed by Russian air power push a brutal assault on rebel-held eastern Aleppo.
The announcement comes as Moscow and Washington gear up for worldwide Syria talks on Saturday, the first since the United States suspended ceasefire negotiations with Russian Federation in protest at the fierce assault on Aleppo.
The newly-appointed Secretary General of the United Nations, has said it breaks his heart to see the suffering of the Syrian people.
But Vitaly Churkin said Friday that Cold War relations between the Soviet Union and Russian Federation more than 40 years ago were different than U.S. -Russia relations today.
As air strikes and shelling of the city's east intensified since Tuesday after a brief period of relative calm, Syria's government approved a United Nations plan to allow aid convoys into most besieged areas of Syria, with the exception of Aleppo.
Russian Federation has faced growing worldwide criticism over the rising civilian death toll in Syria, including Western accusations of possible war crimes.
"I don't think it is right to talk about a new cold war", he said.
The UK is considering military options in the Syrian conflict, but any action would need to be part of a coalition involving the United States, Britain's foreign minister said on Thursday. Syrian government and Russian military aircraft have systematically targeted schools and hospitals in defiance of worldwide law, reducing much of the historic city to rubble.
His remarks come as the United States, Russia and regional powers such as Saudi Arabia, Turkey and Qatar prepare to meet Saturday in Lausanne, Switzerland, for talks on Syria.
At least four children were killed when shells fired by militants hit a school in the government-held area of Aleppo.
There have also been deaths from shelling in government-held areas of Aleppo this week.