Kremlin spokesman Dmitry Peskov has blasted NATO as an "absolutely short-sighted organization" for suggesting Moscow poses a threat to Europe.
"It is absurd to talk about any threat coming from Russia at a time when dozens of people are dying in the center of Europe and when hundreds of people are dying in the Middle East daily," he said.
"We aren't the ones getting closer to NATO's borders," he added.
U.S. President Barack Obama had reassuring words about the European Union in the wake of Britain's "Brexit" vote to leave the bloc.
"We cannot lose sight of the extraordinary achievement that European integration continues to be," he said in Warsaw, flanked by European Council President Donald Tusk and European Commission President Jean-Claude Juncker.
"More than 500 million people speaking 24 different official languages in more than two dozen countries, 19 with a current currency," he said. "Every member of the EU is a democracy. No EU country has ever raised arms against another."
Despite the challenges, Obama said the United States will always have "a strong and enduring interest in a united, democratic Europe."
Russia's state-run news agency Sputnik is stepping up its efforts to discredit NATO and the EU:
NATO chief Jens Stoltenberg said the alliance is boosting its presence on Europe's eastern borders “in response to what Russia did in Ukraine.”
Speaking to journalists, he said Russia has shown it is “willing to use force against sovereign nations in Europe," and denounced Moscow's "illegal" annexation of Crimea.
NATO's response, he said, is “defensive, proportionate, and fully in line with our international commitments."
Stoltenberg: "Today, we will agree to enhance our forward presence in the east of the Alliance. In Estonia, Latvia, Lithuania, and here in Poland. We will deploy, by rotation, a robust, multinational battalion in each of the countries. Making clear that an attack against one Ally will be met by forces from across the Alliance."
A full transcript of his speech is available here.
The BBC reports that hundreds of British troops will be sent to Poland and Estonia as part of NATO's response to potential threats from Russia on Europe's eastern border.