UN officials said they were "appalled" by the escalating violence and urged access to east Aleppo, where more than 250,000 people have been under siege for nearly four months.
Since it began on Tuesday, the assault on the rebel-held east of Aleppo has damaged hospitals, forced schools to close, and killed nearly 100 civilians, according to a monitor.
An AFP correspondent described relentless bombardment with air strikes, mortar rounds and barrel bombs slamming into residential neighbourhoods where residents cowered at home.
US National Security Advisor Susan Rice said Washington condemned "in the strongest terms these horrific attacks against medical infrastructure and humanitarian aid workers."
"There is no excuse for these heinous actions," she said in a statement.
"The Syrian regime and its allies, Russia in particular, bears responsibility for the immediate and long-term consequences these actions have caused in Syria and beyond."
Moscow says it is not involved in the current assault on Aleppo, concentrating its firepower on opposition and jihadist forces in neighbouring Idlib instead.
Once Syria's economic powerhouse, Aleppo has been ravaged by the war that has killed more than 300,000 people since it began with anti-government protests in March, 2011.
No aid has entered east Aleppo since government forces surrounded it in July, and residents report shortages of food and fuel, as well as lengthy power outages and water shortages.
Two top UN officials said they were "extremely saddened and appalled by the recent escalation in fighting in several parts of Syria".
"It is imperative that all parties agree to the plan and allow us to secure immediate, safe and unimpeded access to provide relief to those most in need," they said.
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