“I think they’re using Hungary like they’re using other countries in Europe with nationalist leaderships — to divide the European Union,” said Jiri Pehe, the chief of cabinet to the Czech president, Vaclav Havel, in the 1990s. “It is nice that they’re putting up this facade in Washington on their opening with Hungary, saying that this is an effort towards keeping Hungary in the Atlantic alliance — but this certainly doesn’t contribute to Hungary becoming more Euro-Atlantic.”

“It legitimizes Russian influence in Hungary,” added Mr. Pehe, who is now the director of New York University’s campus in Prague.

With a program to build what he calls an “illiberal democracy,” Mr. Orban is the most influential populist leader in Europe. He has cultivated ties with President Vladimir V. Putin of Russia, called for a “countercultural revolution” inside the European Union, and anointed himself as the protector of Europe’s Christian identity. His critics argue that he has undermined the country’s checks and balances, gerrymandered the electoral map and placed the judiciary under the management of one of his oldest friends.

This record is why Mr. Orban struggled for influence in Washington during the Obama years, despite making a real effort. His government donated millions of dollars to dozens of American research groups, cultural foundations, scholarship funds and lobbyists, much of it funneled through the Hungarian Initiatives Foundation, which is registered as a company in Delaware but owned, according to Hungarian law, by Mr. Orban’s office.

The Hungarian government has endowed the foundation with $15 million, according to official records. Small donations were made to American foreign policy think tanks, including two payments totaling $20,000 to the Center for European Policy Analysis, a Washington-based group led at the time by A. Wess Mitchell, whom Mr. Trump has since appointed as assistant secretary of state for Europe and Eurasia.