PRAGUE — A billionaire turned politician sweeps to power by tapping into deep public disgust with a system that many believe is rigged against them. Even before taking office, he has been hounded by controversy about conflicts of interest related to the company he ran for decades. Opponents threaten to remove him.

If some of that sounds familiar, Andrej Babis, prime minister of the Czech Republic and its second-richest person, has long been compared to Donald J. Trump for his populist politics, bombastic style and exuberant wealth. He has also been similarly besieged by opponents he accuses of being part of an organized cabal out to bring him down.

On Friday, those tensions hit another high point when lawmakers held a vote of no confidence seeking to end Mr. Babis’s government, the second time they have done so since he came to power more than a year ago.

Though Mr. Babis survived the challenge, all sides agree that the conflict has become so venomous that it has paralyzed the politics of this small Central European country at a critical moment when populist forces are threatening to tear apart the democratic gains made since the fall of communism almost 30 years ago.