The newspaper said the dispute intensified after the Polish government sent riot police to secure the Constitutional Tribunal's headquarters on Friday, amid a long-running conflict over control of the court.
Right-wing opponents accused the government of staging a coup.
Russian officials have amplified those accusations. Former Russian president and current Security Council deputy chairman Dmitry Medvedev said on Sunday that a constitutional coup was under way in Poland.
Russian Foreign Ministry spokeswoman Maria Zakharova warned of a possible collapse and tragedy similar to the events in Ukraine in 2014.
The newspaper says the coup allegations have also been promoted by Polish Prime Minister Donald Tusk's domestic right-wing opponents and pro-Russian politicians elsewhere in Europe, including Marine Le Pen in France, Nigel Farage in the United Kingdom and Geert Wilders in the Netherlands.
It also cites Tusk's remarks about “armies of Russian bots” operating online.
The NYT notes that Poland has long been a target of Russian verbal attacks, disinformation campaigns and sabotage operations. It says Russian officials and state media have frequently amplified accusations made by European nationalist and far-left groups against mainstream political forces.
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Source: PAP