During almost two hours of discussions in Reykjavik, Blinken also expressed US concerns on the health of jailed Kremlin critic Alexei Navalny and the "repression" of opposition organisations.
"The Russian president once said that if a fight is inevitable, you need to hit first. But every leader needs to understand that a fight must not be inevitable when it concerns a real war and millions of human lives."
Russia will soon have more than 120,000 troops on Ukraine's border, Ukrainian Foreign Minister Dmytro Kuleba said on Tuesday, calling for new Western economic sanctions on Moscow.
Kyiv, Washington and NATO have been alarmed by the large build-up of Russian troops near Ukraine and in Crimea, the peninsula that Moscow annexed from Ukraine in 2014.
Dmytro Kuleba said rhetoric in Moscow had reached a fever pitch with pundits and officials issuing "dehumanising" statements aimed at intimidating Kiev.