The escalation "would inevitably lead to a further grave deterioration of relations between the EU and Russia," EU foreign affairs chief Federica Mogherini said in a statement.
"Residential areas of the city of Mariupol have been fired upon today from separatist held territory, which has cost the lives of at least fifteen civilians, wounding many others and terrorising the innocent population," the statement said.
"This comes after a series of indiscriminate attacks in the Donbas in the past few days, accompanied by the announcements of further offensives by Russia-backed separatists, who bluntly refuse to observe the cease fire.
That assault has already caused at least 30 deaths and injured 90 people, according to provisional counts AFP obtained from Mariupol municipal spokesman Oleg Kalinin.
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Mogherini called directly on Russia to intercede and halt the carnage.
"I call ... Openly upon Russia to use its considerable influence over separatist leaders and to stop any form of military, political or financial support," her statement said.
"This would prevent disastrous consequences for all. Those responsible for the escalation must stop their hostile actions and live up to their commitments."