WASHINGTON, May 11 -- The United States on Sunday rejected the referendums being held in two regions of eastern Ukraine over their future status, saying it would not recognize the results.

"As the United States has said, the referendums being planned for May 11 in portions of eastern Ukraine by armed separatist groups are illegal under Ukrainian law and are an attempt to create further division and disorder," State Department spokeswoman Jennifer Psaki said in a written statement.

"If these referendums go forward, they will violate international law and the territorial integrity of Ukraine," she added. "The United States will not recognize the results of these illegal referendums."

Earlier in the day, local residents in Ukraine's states of Donetsk and Lugansk went to the polls over whether they want to remain part of Ukraine, despite Russian President Vladimir Putin's call for delayed votes on Wednesday.

Polling started at 8:00 a.m. local time (0500 GMT) and will last till 10:00 p.m. (1900 GMT).

The referendums came after Crimea joined Russia on March 18 following an independence vote on the peninsula that was not recognized by Kiev and the West.

"In addition, we are disappointed that the Russian government has not used its influence to forestall these referenda since President Putin's suggestion on May 7 that they be postponed, when he also claimed that Russian forces were pulling back from the Ukrainian border," Psaki said.

She reiterated that the U.S. had not seen "Russian military movement away from the border."

Washington and its European allies are focusing their efforts on the presidential polls in Ukraine slated for May 25, and have warned Moscow against disrupting the vote.

"The Russian leadership must know that if it continues to destabilize eastern Ukraine and disrupt this month's presidential election, we will move quickly to impose greater costs on Russia," Psaki said.

"The Russian government can still choose to implement its Geneva commitments, as well as follow through on President Putin's statement of May 7," she added. "We call on them to do so."

Armed activists have moved to occupy cities and towns in eastern Ukraine since early April, and the U.S., the European Union (EU), Russia and Ukraine met in Geneva on April 17 over how to de-escalate the tension there.

Kiev has repeatedly blamed Moscow for inciting the unrest and splitting Ukraine. Russia denies the charges, with Putin saying his country will do whatever it can to resolve the crisis and has a positive attitude toward the international community's peace effort.

The U.S. and EU have slapped two rounds of sanctions on Russia over what they called its destabilization moves in eastern Ukraine, targeting individuals and entities with close ties to Putin.

They have threatened tougher sanctions against Moscow by hitting its key sectors of economy including energy, banking and mining.