Stoltenberg said this at a press conference following a two-day meeting of foreign ministers held in Riga.
He said that the situation in the area of the eastern border of Ukraine was discussed.
According to him, "we must remain vigilant and avoid escalation."
“The ministers made it clear that any future invasion or aggression against Ukraine would have a high cost, economic and political consequences for Russia,” RIA Novosti quoted Stoltenberg as saying.
Earlier, Russian President Vladimir Putin suggested starting substantive negotiations to achieve legal guarantees of NATO's eastward expansion.
Putin also noted that if Russia and Ukraine sincerely strive to improve relations, then "no one will experience any threats."