"It's illegal to retaliate against an NLRB charge," he wrote in the email.
Google, a unit of Alphabet Inc based in Mountain View, California, said it could not talk about individual employee cases.
Google chief executive Sundar Pichai told employees in a note on Monday that portions of the anti-diversity memo "violate our Code of Conduct and cross the line by advancing harmful gender stereotypes in our workplace", according to a copy of the note seen by Reuters.
It was not immediately clear what legal authority Mr Damore could try to invoke. Non-union or "at will" employees, such as most tech workers, can be fired in the United States for a wide array of reasons that have nothing to do with performance.
The US National Labor Relations Act guarantees workers, whether they are in a union or not, the right to engage in "concerted activities" for their "mutual aid or protection".
Mr Damore, though, would likely face an uphill fight to seek that protection based on his memo, said Alison Morantz, a Stanford University law professor with expertise in labour law.
"It's going to be a hard sell that this activity was either concerted or for mutual aid or protection, rather than simply venting or pitting one group of workers against the others, which does not sound very mutual," Ms Morantz said.
Debate over the treatment of women in the male-dominated tech industry has raged for months. Claims of persistent sexual harassment in the ranks of Uber Technologies Inc and of several venture capital firms led to management shakeups.
Management at the largest tech firms, including Google, have publicly committed to diversifying their workforces, although the percentage of women in engineering and management roles remains low at many companies.
Mr Damore's memo attacked the idea that gender diversity should be a goal.
"The distribution of preferences and abilities of men and women differ in part due to biological causes and... these differences may explain why we don't see equal representation of women in tech and leadership," Mr Damore wrote in the internal company memo last week.
Google's vice president of diversity, Danielle Brown, sent a memo in response to the furor over the weekend, saying the engineer's essay "advanced incorrect assumptions about gender".