Biden, set to travel to Kiev on April 22, will become the most senior U.S. official to visit the country since the crisis began there.
Secretary of State John Kerry spoke by telephone with Russian Foreign Minister Sergei Lavrov, the State Department said.
Kerry during the call "expressed strong concern that attacks today by armed militants in eastern Ukraine were orchestrated and synchronized, similar to previous attacks in eastern Ukraine and Crimea," said a senior State Department official, speaking on condition of anonymity.
"Militants were equipped with specialized Russian weapons and the same uniforms as those worn by the Russian forces that invaded Crimea. The secretary made clear that if Russia did not take steps to de-escalate in eastern Ukraine and move its troops back from Ukraine's border, there would be additional consequences," the official added.
The official did not state what those consequences would be.
The White House warned Russia against further military action in Ukraine after armed separatists seized government offices in the eastern city of Slaviansk.
"We are very concerned by the concerted campaign we see underway in eastern Ukraine today by pro-Russian separatists, apparently with support from Russia, who are inciting violence and sabotage and seeking to undermine and destabilize the Ukrainian state," said Laura Lucas Magnuson, a spokeswoman for the White House National Security Council.
"We saw similar so-called protest activities in Crimea before Russia's purported annexation," she said in a statement.
She said the United States called on Russian President Vladimir Putin "to cease all efforts to destabilize Ukraine."
In Moscow, the Russian Foreign Ministry said in a statement that Lavrov told Kerry that any armed action by Ukrainian authorities in the east of Ukraine would undermine efforts at a diplomatic solution to the conflict and put planned peace talks at risk. Lavrov said Ukraine was "demonstrating its inability to take responsibility for the fate of the country," according to the Foreign Ministry statement.
Kerry visited Ukraine in March to show support for Ukraine's leaders after Moscow took control of the Crimea region.
Biden, a top adviser to President Barack Obama on foreign policy issues, has been deeply involved in U.S. diplomatic efforts in Ukraine since protests erupted in Kiev in November.
Biden's meetings with Ukrainian government leaders and civil society groups are timed ahead of presidential elections on May 25. He will also discuss energy security issues, the White House said. "The vice president will underscore the United States' strong support for a united, democratic Ukraine that makes its own choices about its future path," the White House said.