The 28 EU ministers also said in a statement that two firms in Russia-annexed Crimea would be hit with asset freezes later Monday.
The ministers agreed to expand the scope of visa bans and asset freezes to target people undermining stability in Ukraine or obstructing international organizations there.
The Obama administration has its own sanctions list that targets several close associates of Russian President Vladimir Putin and their assets for Russia's actions in Ukraine.
France's European affairs minister, Harlem Desir, said additional EU sanctions may be imposed if "actions and provocations" hamper the Ukraine presidential election campaign. He said the 13 people targeted Monday included "Ukrainian separatists and Russian officials."
A total of 61 people are now on the EU's sanctions list due to Ukraine.
Beyond the visa and asset measures, British Foreign Secretary William Hague said it is essential to show Moscow the bloc is ready to step up measures further "depending on Russia's attitude toward the elections" in Ukraine.
France and Germany had already called on Russia to promote de-escalation in Ukraine so its presidential elections could take place May 25. If there is no action from President Vladimir Putin, the EU could increase sanctions, the two nations said.
The EU threw its weight behind efforts of the Organization for Security and Cooperation in Europe set up talks in Ukraine to contain the chaos and violence. France and Germany have already called for a "national dialogue" between the interim government in Kiev and representatives of all Ukrainian regions.
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