Communicating with employees is a bit like building a bank account, according to Alex Gorsky, the chief executive of Johnson & Johnson: making contributions over time, developing a reservoir of trust, because “someday you’re likely going to need to make a withdrawal.”

The topic of trust came up repeatedly on Wednesday, as Mr. Gorsky spoke at the DealBook conference in New York City along with Ginni Rometty, the chief executive of IBM. The 133-year-old Johnson & Johnson brand is under pressure as the company faces more than 100,000 lawsuits over the safety and marketing of products like opioids, transvaginal pelvic mesh implants and the antipsychotic drug Risperdal. More than 15,000 people have sued the company over its talc products, and 33,000 bottles of its baby powder were recently recalled over concerns about asbestos contamination.

Mr. Gorsky has frequently stressed the safety of Johnson & Johnson’s baby powder. On Wednesday, he said that in some cases, “it’s important to take a stand.”