Russia has condemned a fresh round of European Union sanctions and said they would damage efforts to bring the Ukraine crisis to an end.

Russia's foreign ministry urged Western leaders to convince Kiev to hold talks on the future constitutional structure of Ukraine, ahead of presidential elections scheduled for May 25.

The results of the referendums held in eastern Ukraine "should be a clear signal to Kiev of the depth of the crisis" in the country, the foreign ministry said in a statement.

The ad-hoc votes held in the mainly Russian-speaking regions of Luhansk and Donetsk have been dismissed as "illegal" by Western leaders and rejected by Ukraine's interim government.

While the Kremlin has not endorsed the results of the referendums held in eastern Ukraine, Russian leaders said the results highlight the need for dialogue on the shape of the future state.

"Moscow hopes... the EU and United States will use their influence on the current leadership in Kiev so that issues of state structure and respect for the rights of the regions are discussed soon – in any case before the election scheduled for May 25," the Russian foreign ministry said.

The EU announced fresh sanctions against 13 individuals and two companies on Monday in relation to Russia's annexation of Crimea in March. The bloc had already slapped asset freezes and travel bans on 48 Russians and Ukrainians, while the United States has imposed its own separate penalties on Russian individuals and their companies.

Deputy Foreign Minister Grigory Karasin told the EU's Russia envoy on Tuesday that the new sanctions were a "exhausted, trite approach ... that will not only not resolve but will deepen differences, hindering the joint search for a way out of the real crisis situation in Ukraine," the Foreign Ministry said.