US Secretary of State John Kerry has warned his Russian counterpart that Washington will end Syria talks unless Moscow stops the bombing of Aleppo.
In a phone call with Sergei Lavrov, Mr Kerry said the US held Russia responsible for the use of incendiary and bunker bombs against the city.
The US state department said it was making preparations to suspend talks.
Aleppo has come under heavy aerial bombardment since the end of a ceasefire a week ago.
In response to Mr Kerry's phone call, the Russian Deputy Ambassador to the UN, Evgeny Zagaynov, said the "trend" of Russia being blamed for the attacks in Syria must stop.
"It's become a sort of unfortunate tradition that the majority of strikes on civilian facilities in Syria, without checking it ... is blamed on Damascus or Russia,'' he said.
But Moscow said on Wednesday they would send diplomats to Geneva to talk to the US about normalising the situation in Aleppo.
"On orders of the Russian president, we are ready to continue joint work with our American partners on the Syrian issue," the defence ministry said in a statement.
Some 250,000 people are trapped in the rebel-held east of the city. They are under siege from Russian-backed Syrian government forces, which have launched a fierce campaign to recapture the area. The bombardment has been among the worst in the history of the five-year conflict.
The US has accused Russia of taking part in strikes on civilian targets and possibly committing war crimes.
The two nations have been locked in talks in an attempt to revive a fragile peace agreement, but the US said last week that Russia had openly lied to the UN about its intentions.
At least 96 children have been killed and 223 injured in eastern Aleppo since Friday, according to the UN children's agency Unicef.
"The children of Aleppo are trapped in a living nightmare," said Unicef deputy executive director Justin Forsyth on Wednesday. "There are no words left to describe the suffering they are experiencing."
More than 170 people have been killed in east Aleppo since the beginning of the recent offensive, according to the UK-based Syrian Observatory for Human Rights, a monitoring group.
Air strikes continued to hit Aleppo's besieged eastern neighbourhoods on Tuesday night. Local medical workers said that two major hospitals were put out of service by the bombardment.
International medical charity Medecins Sans Frontieres (MSF) tweeted to say that both hospitals were out of service. Adham Sahloul, a spokesman for the US-based Syrian American Medical Society, which supports the two hospitals, said the two attacks took place at the same time, suggesting they were deliberately targeted.
UN Secretary General Ban Ki-moon denounced the reported attacks on the two hospitals as "war crimes".
Addressing crowds in St Peter's Square in Rome on Wednesday, Pope Francis decried the bombing of Aleppo, saying those responsible for killing civilians would have to answer to God.
Aleppo, once Syria's largest city and its commercial and industrial hub, has been divided roughly in two since 2012, with President Bashar al-Assad's forces controlling the west and rebel factions the east.
In the past year, government troops have gradually broken the deadlock with the help of Iranian-backed militias and Russian air strikes. Earlier this month, they severed the rebels' last route into the east and placed its 250,000 residents under siege.
Children in Aleppo have made up a large proportion of casualties from air strikes, according to aid groups. At least 100,000 children remain trapped in the eastern part of the city.
In the government-held west, 49 children were killed by rebel shelling in July alone, the New York Times reports, citing the Syrian Observatory for Human Rights.
On Tuesday, the US pledged to provide an extra $364m (£276m) in humanitarian aid to people affected by the Syrian war.
The World Health Organization (WHO) meanwhile called for the "immediate establishment of humanitarian routes" into Aleppo, where hospitals are running out of supplies and rubble-strewn streets are preventing ambulances from getting through.