Russian-backed separatist rebels and Ukrainian troops have been clashing in the east of the country.
Russia has also been building up troops on the border with Ukraine.
The official, Dmitry Kozak, said that Russian forces could intervene to "defend" its citizens.
"Everything depends on the scale of the conflagration," he said.
He also warned that an escalation could mark the "beginning of the end" for Ukraine - "not a shot in the leg, but in the face".
The United States and Germany have both expressed concern at the increase in tensions.
