WASHINGTON, Nov. 3  -- The White House on Monday condemned the "illegitimate" elections held in parts of eastern Ukraine and threatened to impose more costs on Russia over its further "destabilizing" actions.

Donetsk and Luhansk, two independence-seeking regions in eastern Ukraine, held "presidential and parliamentary elections" Sunday amid criticism from Kiev and the West.

"These sham elections contravened Ukraine's constitution, the law on 'special status,' and the most basic electoral norms," Bernadette Meehan, spokesperson for White House's National Security Council said in a statement.

Meehan reiterated the U.S. stance that "it will not recognize the authority of any individuals claiming to represent parts of Donetsk and Luhansk on the basis of this illegal vote" and accused Russia and "its separatist proxies" of violating the peace agreement signed in Minsk, the Belarusian capital, with Sunday's elections.

Russia's Foreign Ministry said in late Sunday that Moscow respects the expression of the will of people in southeastern Ukraine to vote by election for regional leaders and legislative bodies.

The U.S. is concerned by the statement that "seeks to legitimizes these sham 'elections'," as well as reports that Russia is again moving its troops and military equipment to the border and international monitors have come under attack in recent days, Meehan said.

"More broadly, Moscow's continued failure to fulfill its obligations under the Minsk agreements calls into question its commitment to supporting a peaceful resolution to the conflict in parts of eastern Ukraine," Meehan added.

The spokesperson also called on Russian leaders to adhere to the commitment they made in Minsk and threatened to impose more consequences on Moscow if it continues destabilizing actions.

"Should Moscow continue to ignore the commitments that it made in Minsk and continue its destabilizing and dangerous actions, the costs to Russia will rise," Meehan said.