"Googlers are writing in, concerned about their safety and worried they may be 'outed' publicly for asking a question in the town hall."
He added that comments Google employees had left on a private group had appeared on the wider internet along with their full names.
The company cancelled the open meeting and said it would "find a better way to help our employees connect and discuss these important issues further".
The divisive letter to employees has polarised California's technology industry.
Pichai said Damore's memo was "harmful" and "offensive" to its female employees, and that it would terminate his employment.
Damore has attracted a group of vocal online supporters who claim Google is intolerant to conservative opinions. His advocates include well-known figures of America's alt-right conservative movement, which is planning a protest against Google in at least five US cities later this month.
The former Google engineer has become a cult figure online, responding to the firm in a YouTube interview with right-wing hosts and posing for photos outside its offices holding a sign that said "Fired for truth" and wearing a T-shirt with an altered logo "Goolag".
Damore, who denied believing in gender stereotypes, has threatened Google with legal action. The row comes as Google is under investigation by the US Department of Labor for having a "systemic" and "extreme" gender pay gap. Its most recent diversity report revealed 31pc of its employees are women, who account for 25pc of its leadership roles.