WASHINGTON, April 7 -- Any further Russian efforts to destabilize Ukraine will incur costs for Russia, U.S. State Secretary John Kerry warned Russian Foreign Minister Sergei Lavrov on Monday.

Kerry told Lavrov in a phone call that the United States is watching events over the past 24 hours in eastern Ukraine with " great concern" and noted that these "do not appear to be a spontaneous set of events," State Department spokeswoman Jen Psaki said at a press briefing.

Noting Ukraine's assertion that the events "appeared to be a carefully orchestrated campaign with Russian support," Kerry urged Russia to "publicly disavow the activities of separatists, saboteurs and provocateurs," according to Psaki.

Pro-Russia activists seized several government buildings in eastern Ukraine on Sunday, demanding closer ties with Moscow and a referendum to give more powers to local authorities. Ukrainian Prime Minister Arseny Yatsenyuk accused Russia of stirring up the unrest, which was rejected by Moscow.

"Stop blaming Russia for all of Ukraine's problems. Ukrainian people want to hear meaningful answers from official Kiev," the Russian Foreign Ministry said in a statement posted on its website.

Moscow warned that Ukraine should "face new crises and difficulties" unless its irresponsible politicians make the necessary reforms to pacify its eastern regions, according to the statement.

The events in eastern Ukraine proved the need to hold a constitutional reform in the country and to federalize it, the Russian Foreign Ministry said.

Meanwhile, the White House also expressed U.S. concerns about " escalatory moves" in Ukraine over the weekend.

"If Russia moves into eastern Ukraine, either overtly or covertly, this would be a very serious escalation," White House spokesman Jay Carney told a press briefing.

Carney said there is strong evidence suggesting some of the demonstrators who have taken over government buildings in the eastern Ukrainian cities "were paid and were not local residents."

"We are prepared to impose further sanctions on sectors of the Russian economy should the situation escalate," he added.

Kerry and Lavrov also discussed convening direct talks within the next 10 days between Ukraine, Russia, the United States and the European Union to try to de-escalate the tension, said Psaki.

Discussion about the right timing and agenda for the four-way talks will continue, she added.