But Mr. Trump’s efforts ring familiar to many who have studied authoritarian regimes in countries around the world, like those run by President Vladimir V. Putin in Russia and Prime Minister Viktor Orban in Hungary.

“Trump’s attempt to overturn the election, and his pressure tactics to that end with Brad Raffensperger, the Georgia secretary of state, are an example of how authoritarianism works in the 21st century,” said Ruth Ben-Ghiat, author of “Strongmen: From Mussolini to the Present.” “Today’s leaders come in through elections and then manipulate elections to stay in office — until they get enough power to force the hand of legislative bodies to keep them there indefinitely, as Putin and Orban have done.”

The call with Mr. Raffensperger, which was recorded and released to the news media after Mr. Trump tweeted a false version of the conversation, provided a breathtaking case study of how far the president is willing to go to preserve power. He ran through one unfounded conspiracy theory after another, pushed Mr. Raffensperger to “find 11,780 votes” to flip the election outcome, appealing to him as a Republican to show loyalty and implicitly threatening criminal charges if he refused.

“So what are we going to do here, folks?” Mr. Trump said at one point. “I only need 11,000 votes. Fellas, I need 11,000 votes.”

The call was unseemly enough that even some of the president’s allies distanced themselves. “One of the things, I think, that everyone has said is that this call was not a helpful call,” Senator Marsha Blackburn of Tennessee, one of the Republicans pushing to reject Biden electors from swing states, conceded on Fox News.