Eric Grosse, vice president of security engineering, made the announcement on a company blog, The Washington Post reported. He said the attacks could involve the installation of malicious software or "phishing," attempts to get information through a fake Web site.
Google's message will read: "Warning: we believe state-sponsored attackers may be attempting to compromise your account or computer. Protect yourself now."
Grosse said recipients of the message will not necessarily have been attacked, but should change passwords and update browsers.