MOSCOW — The Kremlin, increasingly convinced that President Trump will not fundamentally change relations with Russia, is instead seeking to bolster its global influence by exploiting what it considers weakness in Washington, according to political advisers, diplomats, journalists and other analysts.

Russia has continued to test the United States on the military front, with fighter jets flying close to an American warship in the Black Sea this month and a Russian naval vessel steaming conspicuously in the Atlantic off the coast of Delaware.

“They think he is unstable, that he can be manipulated, that he is authoritarian and a person without a team,” Alexei A. Venediktov, the editor in chief of Echo of Moscow, a liberal radio station, said of President Trump.

The Russian president, Vladimir V. Putin, has long sought to crack the liberal Western order, both as a competitor and as a champion of an alternative, illiberal model. To that end, he did what he could to buttress the electoral chances of Mr. Trump, who seemed like a kindred spirit with his harsh denunciations of NATO and the European Union, his endorsement of the British withdrawal from the European Union and his repeated shrugs over Russia’s destabilizing Ukraine.