BRUSSELS—The European Union on Saturday issued its sharpest warning of a fresh spike in tension with Russia, as violence continued to escalate in eastern Ukraine.

In a statement following attacks on residential areas in the city of Mariupol, the EU’s foreign policy chief Federica Mogherini called on Russia to use its “considerable influence” with the rebels to calm the situation and stem its support for pro-Moscow separatists.

“This further escalation of the open armed conflict has tragic consequences for a population greatly suffering already for far too long. It would inevitably lead to a further grave deterioration of relations between the EU and Russia,” Mogherini said.

Russia denies western accusations that it is giving financial, political and material support to the rebels, who have been battling Ukrainian armed forces. The Kremlin also has denied Kiev’s assertion that it has thousands of troops in its neighbor’s territory.

Mogherini’s warning on Saturday marks a substantial sharpening in approach by Brussels toward Russia. On Monday, Mogherini led a debate among foreign ministers looking at how to soften tension with Russia over time and exploring conditions under which EU sanctions could be wound back.

Earlier this week, Edgar Rinkevics, foreign minister of Latvia, which holds the rotating EU presidency, warned the bloc could tighten sanctions on Russia if violence continued. Privately, diplomats in other major EU countries also have said there is fresh consideration being given to possibly tightening pressure on Moscow.

The EU’s standing sanctions on Russia expire between March and July and need the backing of all 28 member states to be renewed.

Russian President Vladimir Putin has acknowledged that those measures have helped worsen Russia’s economic situation.

An expanded version of this report is available at wsj.com