BUDAPEST—Hungarian lawmakers on Monday passed amendments to the country's constitution, despite warnings from the European Union and the U.S. that the measures could threaten the rule of law and weaken democratic checks and balances.

Parliament, controlled by Prime Minister Viktor Orban's right-leaning Fidesz alliance, approved the changes—including provisions that allow the court system's top administrator and prosecutors to choose which judges hear legal cases—in a party-line vote.

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