Ukraine's president says intercepted radio and telephone conversations prove that pro-Russian rebels were responsible for firing rockets that pounded Mariupol and killed at least 30 people.
The attack on Mariupol, a strategically situated port city that had been relatively quiet for months, is likely to further aggravate relations between the United States and Russia.
Putting the blame squarely on Moscow, President Barack Obama said the US would work with its European partners to "ratchet up the pressure on Russia".
European Union foreign affairs chief Federica Mogherini later announced that EU foreign ministers would hold an "extraordinary" meeting in Brussels on Thursday to discuss Ukraine.
Diplomats said the UN Security Council would meet on Monday afternoon on Ukraine.
"The intercepted radio and telephone conversations, which were given to me by Ukraine's security services, irrefutably prove that the attack was conducted by the terrorists, who, unfortunately, are supported by Russia," President Petro Poroshenko said during an emergency meeting of his Security Council.
The Organisation for Security and Co-operation's monitoring mission said on Saturday that the Grad and Uragan rockets that hit Mariupol were fired from areas under rebel control.
The OSCE said its Permanent Council would meet on Monday in Vienna "in light of the rapid deterioration of the situation in eastern Ukraine".
In Mariupol on Sunday, emergency workers disposed of rocket fragments left by the attack.
Police said two unexploded rockets were found in a bank and an apartment building.
Russian Foreign Minister Sergei Lavrov, speaking separately with Mogherini and US Secretary of State John Kerry, attributed the latest violence to stepped-up operations by the Ukrainian military.
He urged the US and its allies to pressure Ukraine to engage in comprehensive talks for a political solution to the conflict, ministry statements said.
Kerry told Lavrov that the US was ready to participate in serious efforts to settle the conflict, but made clear that "Russia will be judged by its actions and that the costs to Russia will only increase if attacks continue," the US State Department said.
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