WASHINGTON — Secretary of State John Kerry agreed Monday to meet with top diplomats from Russia, Ukraine and the European Union in a new push to calm tensions in eastern Ukraine, as the White House threatened further sanctions if Moscow intervenes.

Kerry’s meeting with his counterparts will take place in the next 10 days, the State Department said, and comes amid mounting U.S. concern that Russia could build on its recent annexation of Crimea by trying to split off other areas of Ukraine. To that end, the White House issued a warning to Russian President Vladimir Putin.

“If Russia moves into Eastern Ukraine, either overtly or covertly, this would be a very serious escalation,” White House spokesman Jay Carney said, adding that the U.S. is “prepared to impose further sanctions on sectors of the Russian economy should the situation escalate.”

Pro-Russian activists who have barricaded inside a government building in eastern Ukraine proclaimed the region independent, while calling for a referendum on seceding from Ukraine — a chain of events with ominous echoes of the prelude to Russia’s annexation last month of Crimea. The Ukrainian government has vowed to quell the unrest despite the tens of thousands of Russian troops stationed along their joint border.