BERLIN—The day Volkswagen AG’s lawyers were in court sealing a historic $15 billion settlement to resolve its emissions scandal in the U.S., Chief Executive Matthias Müller went to Brussels to try to defuse a potential flare up with the European Commission over demands that the German car maker also offer generous compensation for nearly nine million European customers.

During the meeting on Thursday with Elzbieta Bienkowska, the European Union Industry Commissioner, Mr. Müller made clear that Volkswagen had no intention of...