The U.S. and UK have warned the Syrian and Russian governments that new economic sanctions could be imposed if the bombing of Aleppo continues, according to BBC News.
U.S. Secretary of State John Kerry described the situation as "the largest of humanitarian disasters".
He said that Russia needed to understand that "this war cannot end without a political solution".
Kerry is in London taking part in talks aimed at finding a peaceful solution to the Syria conflict.
Speaking alongside the UK's Foreign Secretary Boris Johnson, he said that "crimes against humanity" were taking place daily in Aleppo.
Johnson also urged Russia to "do the right thing by humanity and the people of Syria" by committing to a ceasefire.
"It needs a ceasefire and it means getting back to the negotiating table in Geneva," he said.
"These things will eventually come to bite the perpetrators of these crimes and they should think about it now," Johnson added.
He said that as part of measures designed to "keep the pressure up", additional sanctions on the Syrian regime "and their supporters" were under consideration.
A ceasefire in Syria brokered last month collapsed after just a few days.
Since then Syrian forces, backed by Russia, have been bombing the city of Aleppo – the most high-profile battleground in the country's civil war – in what Washington has called a war crime.
Aid agencies say a 72-hour ceasefire is urgently needed to allow supplies in and civilians out of devastated areas in the rebel-held and government-besieged east of the city, where 275,000 people live.
On Saturday Russia and the U.S. were joined at peace talks in Lausanne, Switzerland, by countries which back opposing sides in the war.
Representatives from Saudi Arabia, Iran, and Turkey were there. Iranian troops are currently supporting Syrian forces, while Saudi Arabia is arming the opposition.
After five hours in Switzerland negotiations broke up with no agreement on an end to the bombing of Aleppo or on aid for Syria's besieged towns. But all the diplomats agreed to continue talking.
