Ms. Vestager feigns to hardly remember the president’s comment. “Since I know the very good relationship I have with the United States, then he must only meet people who really like the States if I am the one who likes you the least,” she said.

If anything, American authorities are coming around to share her tech skepticism. Federal, state and congressional investigators are scrutinizing the tech industry over unfair business practices. Ms. Vestager said she saw opportunities to collaborate, but was waiting to see how the inquiries unfolded.

“Obviously it’s very interesting to see what will come of it,” she said.

As the United States begins to investigate Amazon, Apple, Facebook and Google, some American officials are trying to learn lessons from Europe’s efforts. The investigations of Google and others took years to complete, giving the companies extra time to solidify their dominance. And once the inquiries were completed, critics said, the penalties focused on large fines that the companies could easily afford, rather than enforcing structural changes that would restore competition.

Luther Lowe, the head of public policy at Yelp, the reviews website that has been a frequent critic of Google’s behavior, praised Ms. Vestager’s efforts. But he said companies like Yelp “have to date still not seen a shred of practical relief, despite having prevailed in concept.”

Ms. Vestager needs to use all powers at her disposal, he said, “or be granted new ones.”

Ms. Vestager said some of the criticism was valid. She is taking steps to speed up investigations and is applying a rarely used rule known as “interim measures,” that acts as a cease-and-desist order for companies to stop acting a certain way while an investigation can be conducted.

She will play a leading role in the E uropean Union’s debate over a new Digital Services Act, which could bring sweeping reforms to how the internet operates, including forcing online platforms to remove illegal content or risk fines and other penalties. Facebook, she said, must be quicker to stop the spread of false and mi sleading information, violent material and hate speech.

“You have to take it down because it spreads like a virus,” she said. “But if it’s not fast enough, of course, eventually we will have to regulate this.”