The Democratic presidential candidate called on the FBI director to explain the new inquiry to the American people.
James Comey earlier said the FBI was looking into newly found messages.
The latest emails came to light during a separate inquiry into top Clinton aide Huma Abedin's estranged husband, former congressman Anthony Weiner.
Devices belonging to Abedin and Weiner were seized in a separate FBI inquiry into whether he sent sexually explicit emails to a 15-year-old girl in North Carolina.
"The American people deserve to get the full and complete facts immediately," said Hillary, in her first public comments on the issue.
"It's imperative that the bureau explain this issue in question, whatever it is, without any delay."
She highlighted that Comey had said "he doesn't know whether the emails referenced in his letter are significant or not", adding: "I'm confident (that) whatever they are will not change the conclusion reached in July."
Comey said the FBI would investigate if the newly discovered emails contain classified information.
The FBI chief said in a letter to Congress that investigators had discovered the emails "in connection with an unrelated case... that appear to be pertinent to the investigation".
He said he "cannot yet assess whether or not this material may be significant, and I cannot predict how long it will take us to complete this additional work".
The FBI has already established the Democratic candidate had classified information on a private email server.
In July, Comey said Hillary's handling of sensitive material during her 2009-13 tenure as secretary of state was "extremely careless", but cleared her of any criminal wrongdoing.
The revelation that she handled sensitive information while breaking federal rules by running her own email server out of her upstate New York home has dogged her campaign since last year.