EU foreign policy chief Federica Mogherini and humanitarian commissioner Christos Stylianides said in a statement: "The indiscriminate suffering being caused among innocent civilians... is an unacceptable breach of international humanitarian law."
They denounced the "fire-bombing and shelling" as well as the "deliberate targeting" of a humanitarian convoy last week and the "cutting off of water supplies to the majority of civilians still in the city."
The aid convoy was hit by an airstrike that US officials have said was carried out by Russian planes backing President Bashar al-Assad's regime.
UN officials say nearly two million civilians were left without water in the devastated northern city after regime bombardment damaged a pumping station and rebels shut down another in retaliation.
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Syria's Aleppo reels from air strikes, UN chief 'appalled'
In their statement dated Brussels, Mogherini and Stylianides called the suffering caused by the attacks "an affront" to the whole world.
"It risks to take us ever further from a negotiated settlement of the conflict, which remains the only way of bringing it to an end," they added.
The pair called on those with influence on the regime and those dealing with the armed opposition "to apply the maximum pressure to cease the attacks."
They also urged them to work to "allow unhindered and continuous humanitarian access to those in need, and resume political negotiations under the auspices of the UN in Geneva as swiftly as possible."
A truce deal negotiated between Moscow and Washington brought a few days of respite in Aleppo earlier this month, but no humanitarian aid before its total collapse this week.
Aleppo reels from air strikes
UN chief Ban Ki-moon said he was "appalled by the chilling military escalation" since the Syrian army on Thursday announced the launch of an offensive backed by Russian air raids to oust rebels from eastern Aleppo that has cost around 100 lives.
The use of bunker buster bombs and other advanced munitions against civilians may amount to war crimes, he warned.
Voicing indignation, US Secretary of State John Kerry who failed in talks this week with Russian counterpart Sergei Lavrov to revive a ceasefire said: "What is happening in Aleppo today is unacceptable. It is beyond the pale."
"If people are serious about wanting a peaceful outcome... they should cease and desist bombing innocent women and children, cease cutting off water and laying siege in mediaeval terms to an entire community," he said.
Kerry had harsh words for Moscow's involvement in the conflict, in comments at a meeting with his European counterparts.
"Russia needs to set an example, not a precedent -– an unacceptable precedent, I might add, for the entire world," he said.
Syria's Foreign Minister Walid Muallem, for his part, told the UN General Assembly that the army and its allies were making "great strides" in the conflict.
UN Security Council to meet over Aleppo
The UN Security Council will meet to urgently address the crisis over fighting in Aleppo, after a request from US, Britain and France, diplomats say.
The crisis meeting is scheduled for 1500 GMT on Sunday (0100 on Monday).
Syrian government forces have seized ground from rebels north of Aleppo, tightening their siege on the city's opposition-held east as it came under fierce air strikes in a major offensive by the Russian-backed army.
Dozens of people have been reported killed in eastern Aleppo since the army announced the new offensive late on Thursday, burying any remaining hope for reviving a ceasefire brokered by the United States and Russia.
Residents of rebel-held eastern Aleppo say it is being subjected to the most ferocious bombardment of the war.
Rebel officials said heavy air strikes on Saturday hit at least four areas of the opposition-held east, home to more than 250,000 people. Rebels say the strikes are mostly being carried out by Russian warplanes.
