ST. PETERSBURG, RUSSIA—Russian President Vladimir Putin accused the Trump administration of using tariffs and sanctions to maintain dominance of the global economy, while highlighting the Kremlin’s increasingly warm ties with China, as the two countries’ relationship with Washington deteriorates.

During an address at Russia’s flagship annual economic forum, Mr. Putin blasted the Trump administration’s use of tariffs—including those Washington has slapped on China—as a strong-arm tactic that is provoking a crisis in international...