WASHINGTON — President Trump hopes to meet with President Vladimir V. Putin of Russia in the next few weeks even as the American leader increasingly clashes with European allies over how to counter Moscow’s assertive actions in Europe and the Middle East.

Mr. Trump is sending his national security adviser, John R. Bolton, to Moscow next week to discuss a possible meeting. Mr. Trump is already scheduled to attend a NATO summit meeting in Brussels next month, followed by a long-delayed visit to Britain. He could presumably add a stop in another country like Austria to see Mr. Putin.

Mr. Trump has been eager to get together with Mr. Putin for months despite increasing tension in the relationship between Russia and the West. Just two weeks ago, Mr. Trump urged the rest of the Group of 7 major industrial powers to readmit Russia, which was expelled in 2014 after its armed seizure of Crimea from Ukraine. But the other members rejected the idea, deeming it inappropriate.

By meeting with Mr. Putin on his own anyway, Mr. Trump would send a signal to European leaders that he does not intend to be held hostage to their approach to Moscow, adding another rupture to his fights with the United States’ traditional allies over tariffs, security and migration. In recent public comments, he has emphasized the importance of building a friendly relationship with Mr. Putin and minimized the continuing dispute over Ukraine, blaming Russia’s actions on former President Barack Obama.