Putin's comments came as U.S. President Joe Biden and British Prime Minister Boris Johnson spoke about Johnson's trip last weekend to Ukraine.
The White House said the two leaders "affirmed their commitment to continue providing security and humanitarian assistance to Ukraine in the face of ongoing atrocities by Russia" and "welcomed ongoing cooperation with allies" in imposing sanctions on Russia "for its unprovoked and unjustified war."
Ukraine, despite massive Russian attacks on some cities and destruction of hospitals and housing, has thwarted Moscow's attempted overthrow of the Ukrainian government, with Russia now concentrating its attacks on eastern Ukraine.
Putin said Russians' resolve against the Western sanctions will grow stronger and that "the Russian people always strengthen their unity in a difficult situation."
The Russian leader said that "common sense should prevail," adding that the West should "come back to reason and make well-balanced decisions without losing its face."
Putin said the West, on a day the United States announced its highest inflation rate in 40 years, will be shaken by surging consumer prices. He called European leaders stooges of U.S. policymakers in Washington who are harming their own countries by supporting Ukraine.
Some Western leaders have called for war crimes investigations of Putin. Ukrainian President Volodymyr Zelenskyy urged the European Union to sanction all Russian banks and halt imports of Russian oil, as he issued his latest appeal Tuesday for support in ending Russia's invasion of Ukraine.
Speaking by video to lawmakers in Lithuania, Zelenskyy said if European nations continue to trade with Russia, then Russian leaders "know they will go unpunished."
EU members have issued multiple rounds of sanctions targeting Russian officials and businesses but have been reluctant to quickly cut off imports of Russian gas and oil as Zelenskyy has urged.
Some European leaders have expressed concerns about how such actions would affect their economies due to their reliance on Russian energy supplies.
Ukraine said Tuesday that Russian forces are trying to secure control of the besieged southern port city of Mariupol while preparing for expanded operations in the eastern Donetsk region.
The assessment came as Britain's Defense Ministry said it expects fighting in eastern Ukraine "will intensify over the next two to three weeks as Russia continues to refocus its efforts there." A ministry statement said Russia is withdrawing more of its forces from neighboring Belarus and redeploying them to eastern Ukraine.
Zelenskyy said in a video address late Monday he fears Russia could use chemical weapons in Ukraine and urged the West to impose more severe sanctions against Russia to prevent it from using such weapons.
Pentagon press secretary John Kirby said the United States cannot confirm reports that chemical weapons have already been used, but said if true, they "are deeply concerning."
He said the reports are "reflective of concerns that we have had about Russia's potential to use a variety of riot control agents, including tear gas mixed with chemical agents in Ukraine."
Some information for this report came from The Associated Press, Agence France-Presse and Reuters.