BRUSSELS — President Vladimir V. Putin of Russia arrived in Austria on Tuesday sensing an opportunity almost unimaginable just months ago: to overhaul frosty relations with a European Union infuriated by President Trump on a host of issues, from climate and Iran to, most recently, tariffs and trade.

Never mind that Mr. Putin was until recently virtually a pariah in Europe after his military interventions in Ukraine, Crimea and Syria; after meddling in European elections and working hard to foment right-wing populist uprisings throughout the Continent; after polluting the political environment with fake news; and after allegedly poisoning a former Russian spy and his daughter in Britain, charges Russia denies.

Mr. Putin was now gaining considerable traction by casting himself as a reliable friend and trading partner to Europe even as the Trump administration was treating its closest allies there as strategic and economic competitors.

“It is not our aim to divide anything or anybody in Europe,” Mr. Putin said in a television interview before he went to Vienna. “On the contrary, we want to see a united and prosperous European Union because the European Union is our biggest trade and economic partner. The more problems there are within the European Union, the greater the risks and uncertainties for us.”