BUDAPEST — Facing a floor-to-ceiling window that offered sweeping views of the Danube, the river that flows through 10 European countries, Aleksander Ceferin paused for a moment to consider his words.

Ceferin, a Slovenian lawyer elected in February to a second term as the leader of UEFA, European soccer’s governing body, has become accustomed to carefully tempering his comments, to steering clear of trouble in whatever he chooses to say publicly, but this month he knows his every word will be parsed even more than usual.

[Sign up for Rory Smith’s weekly newsletter on world soccer: Rory Smith on Soccer.]

In the past week alone, UEFA has found itself fighting fires on three fronts. First, there was criticism of a behind-the-scenes effort to reshape the Champions League, club soccer’s most important competition and UEFA’s financial engine, by effectively excluding most of Europe from the tournament. Then came anger from England over the choice of Azerbaijan’s capital, Baku, as the host of next week’s Europa League final. But the loudest fury arrived on Monday, when the newly crowned English champion Manchester City learned, through a report by The New York Times, that it could be facing a Champions League ban related to an investigation into its finances.

Each problem sat squarely on the desk of Ceferin last week in his temporary office, a converted suite in a luxury hotel in Budapest. And each will test his ability to balance the competing interests of rich clubs and small leagues, to defend his integrity amid serious accusations from powerful interests, and to navigate a difficult moment for European soccer in which some are questioning UEFA’s ability — and even its willingness — to enforce its rules.