MOSCOW/BEIJING, May 13 -- Russia said Monday it respects the choice of people in Donetsk and Lugansk regions in Ukraine, who voted overwhelmingly in favor of independence on Sunday, amid continuous rejection and severe criticism from Kiev and Western countries.

"We have taken note of high voter turnout despite attempts to derail the voting and we condemn the force used, including military hardware, against civilians, which lead to fatalities," the Kremlin press service said in a statement.

It added that Russia had been carefully monitoring the preparation and the course of the referenda.

Moscow called for dialogue between Kiev authorities and the two regions, saying "all mediation efforts, including by the Organization for Security and Cooperation in Europe, are welcome."

Sergei Naryshkin, speaker of the Russian State Duma, or the lower house of parliament, said the referenda "show their (local residents') wish to defend their rights, essentially, their wish to be free."

Russian Foreign Minister Sergei Lavrov on Monday blamed the United States and Ukraine for hampering the release of proposals on solving the Ukrainian crisis drafted by the Organization for Security and Cooperation in Europe (OSCE).

"Somebody in Washington and Kiev is against involvement of (East Ukrainian) regions in the dialogue, and this is why the roadmap drawn up by the OSCE chair is not disclosed," he said.

"This is another evidence that Kiev has yet to realize the need to talk to its own people," he added.

Also on Monday, China called for a solution to the Ukrainian crisis under a framework of law and order.

China has always followed the policy of no interference in the internal affairs of others, said Foreign Ministry spokeswoman Hua Chunying at a daily press briefing in response to referendums held in the two regions of eastern Ukraine over their future status on Sunday.

Hua said China respects Ukraine's sovereignty and territorial integrity.

Sunday's referendums, however, drew criticisms from Kiev and the West, which rejected the self-rule votes as illegal.

The United States reiterated on Monday that it does not recognize the referenda held in Donetsk and Lugansk in favor of independence.

"We do not recognize the illegal referendum that took place in portions of Donetsk and Lugansk over the weekend," State Department spokeswoman Jennifer Psaki told reporters at a daily news briefing.

Commenting on the referenda, a spokesperson of the British Foreign and Commonwealth Office said on Sunday that the result was "regrettable."

"The UK agrees that we should all work together to restore stability, security and prosperity in the region," the spokesperson noted.

As for Germany and France, German Chancellor Angela Merkel and French President Francois Hollande on Saturday said the referenda were illegal in a joint statement.

Following the Foreign Affairs Council meeting Monday, the European Union said in a statement the referenda in eastern Ukraine was "illegitimate."

For his part, Ukraine's acting President Olexandr Turchynov rejected the referenda, saying the recent events were Russia's plan aimed at destabilizing the situation in his country.

In its Sunday's statement, the Ukrainian Foreign Ministry said "the organizers of this criminal farce have violated the constitution and Ukrainian law."

Local residents in Donetsk and Lugansk went to the polls Sunday in separate referenda over the regions' future status. Preliminary returns showed that some 89.07 percent of voters in Donetsk cast ballots in favor of independence from the government in Kiev.

In Lugansk, referendum organizers said about 96 percent of voters backed the region's sovereignty.

According to organizers, the turnout for the referenda in the two regions was 74.87 percent and 75 percent, respectively.