"The conflict on the borders is on the verge of getting deeper and tensions have been building up with respect to the European security as a whole," Borrell told reporters.
The EU has a firm stance and a strong commitment "that any military aggression against Ukraine will have massive consequences and severe costs," he added.
The Kremlin did not immediately issue a public response to Borrell's visit. Moscow has previously denied planning a new military offensive against Ukraine and accuses Kyiv of building up its own forces in the east of the country.
Russia has pressed the United States for security guarantees that NATO will halt its eastward expansion. The two sides will meet for talks in Geneva on January 9-10.
