US Secretary of State John Kerry is threatening to cut off all contact with Moscow over Syria, unless Russian and Syrian government attacks on Aleppo end.
The State Department said Mr Kerry issued the ultimatum in a Wednesday telephone call to Russian Foreign Minister Sergey Lavrov.
Mr Kerry's spokesman, John Kirby, said he expressed grave concern over Russian and Syrian government attacks on hospitals, water supplies and other civilian infrastructure in Aleppo.
He said Mr Kerry told Mr Lavrov that the US holds Russia responsible for the use of incendiary and bunker-buster bombs in an urban area.
Mr Kerry told Mr Lavrov the US was preparing to "suspend US-Russia bilateral engagement on Syria", including on a proposed counter-terrorism partnership, "unless Russia takes immediate steps to end the assault on Aleppo" and restore a ceasefire.
Meanwhile, UN chief Ban Ki-moon says the situation in rebel-held parts of Aleppo is worse than a "slaughterhouse" and implicitly accused Syria and Russia of committing war crimes.
He spoke to a UN Security Council meeting Wednesday on health care in armed conflict as two more hospitals were struck in the city's besieged east.
Without naming countries, Mr Ban said "those using ever more destructive weapons know exactly what they are doing - they know they are committing war crimes".
The Syrian government announced the offensive to retake rebel-held eastern Aleppo, and the only countries carrying out airstrikes are Syria and Russia.
Mr Ban said: "Hospitals, clinics, ambulances and medical staff in Aleppo are under attack around the clock."
He said there must be "action," and "accountability", adding: "International law is clear. Medical workers, facilities and transport must be protected. The wounded and sick, civilians and fighters alike, must be spared. Deliberate attacks on hospitals are war crimes."