At the hearing, Mr. Simons and other commissioners would not discuss the Facebook investigation, which is not completed. But comments from F.T.C. commissioners provided insight into their thinking on privacy cases.

The two Democratic commissioners said a punishment should send a strong message that a tech company in violation of privacy rules must change behavior. And in some cases, the F.T.C. should name top executives as liable parties, they said.

“For some firms fines are a parking ticket and the cost of doing business and cannot change behavior unless penalties are painful and finding out who at the top called the shots,” said Rohit Chopra, one of the Democratic commissioners.

Mr. Chopra added that strong enforcement should include “looking at the role of individuals who made the decision that it was worth violating the law in order to profit.”

The issue of executive responsibility has been a divisive topic during the F.T.C.’s settlement negotiations with Facebook, according to two people familiar with the decision. At one point, F.T.C. officials proposed naming Facebook’s chief executive, Mark Zuckerberg, as a responsible party. That would subject him to financial and other penalties if Facebook ran afoul of privacy rules in the future. Mr. Zuckerberg is not expected to be made personally responsible in a final settlement.

[Read more: Facebook faces a big penalty, but regulators are split over how big.]

Republican members warned of going too far with a new privacy law.

Christine Wilson, one of the three Republican commissioners, said there could be “unintended consequences,” and added that some privacy laws could be more burdensome on small companies than tech giants like Facebook and Google.