Recent reports have suggested that the Federal Trade Commission may be preparing to sue Google (GOOG) for antitrust violations. “I think we’ve had a pretty good debate with regulators,” Page said during an on-stage question and answer session at Google’s Zeiggest conference in Paradise Valley, Arizona. “We’ve taken an approach to work with them.” He said he hoped that approach would continue to be constructive.

But Page said he feared over-regulation of the Internet could be a risk for Google. He specifically singled out the company’s new privacy policy, which allows it to access a person’s data across various Google services, as essential to the functioning of some of the company’s most advanced offerings. Earlier this week, European privacy regulators asked Google to alter that policy.

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While Page has been active inside Google and has spoken recently to a private gathering of advertising executives, he had not participated in a public event since problems with his vocal cords surfaced several months ago. Google announced in June that Page had “lost his voice” and would skip the company’s developer conference, its quarterly earnings call with financial analysts and other events. Page’s voice was hoarse on Tuesday, but he appeared healthy. He refused to answer a reporter’s question about his health, saying he was “here and talking.”

Page, who took over as CEO 18 months ago, said Google would continue to focus on long-term technical challenges that can impact lots of people. “I get really excited about things we can do at Google to really seriously change the world,” he said. “We did that with search. We tried that with books. We are trying all variety of things.”

He highlighted the company’s work on digital maps, Android, and driverless cars, as examples of the kind of long-term bets that Google focuses on. And he took digs at two of Google’s biggest rivals, Apple (AAPL) and Facebook (FB).

After extolling the virtues of Google’s multi-year effort to develop an accurate digital representation of the real world with its mapping services, he said the company was “almost there.” In a clear reference to Apple’s embarrassing rollout of a mapping application that was riddled with errors, he added: “We are we are excited that other people have started to notice that we’ve worked hard on that for 7 years.”

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He said it was “likely” that Google would try to make its maps available on Apple devices, despite its lack of control over how they would appear or be distributed.

And in a pointed criticism at Facebook refusal to open up its data to outside parties, including Google’s search engine, he said the Internet worked best when essential data was shared across companies. Speaking specifically about social data, he said: “I would love to make use of that in any way we can.”