He said Georgians have clear options.
Abrams' opponent Brian Kemp denounced the robo-calls as "vile".
Polls suggest Kemp and Abrams are locked in a tight race in a contest that has taken on historic significance because of the potential of Abrams becoming the nation's first black female governor. A last-minute fracas about the state's voting system raised the specter of a disputed result.
The Georgia race has been tainted by accusations of voter suppression under Kemp and racially charged remarks directed at Abrams.
Last month, a federal judge endorsed plaintiffs' arguments that Kemp has been derelict in his management of the state election system and that the setup is lacking in reliability.
Neither Cross nor the state party went public.
The initial email in the exchange is from a man who was outlining vulnerabilities in the Secretary of State's website. Since then, she's been a fundraising juggernaut, raising millions from beyond Georgia, and she's drawn a parade of notable supporters, most recently former President Barack Obama and media icon Oprah Winfrey.
With the clock winding down before Tuesday's vote, Georgia's chief elections officer, who is also running for governor, turned a report of an alleged vulnerability in the election system he oversees into a political weapon in a race he is hoping to win.
That didn't stop Kemp's office from posting a notice on Georgia's Secretary of State website, which voters visit to check their registration status or find their polling place.
According to AP interviews and records released by the Georgia Democratic Party, a lawyer for election-security advocates, David Cross, notified both the Federal Bureau of Investigation and Kemp's counsel Saturday that a citizen had alerted him to the flaw.
"After learning of a failed attempt to hack the state's online voter registration and My Voter Page, my office contacted the Department of Homeland Security and opened an investigation", Kemp said in a brief posting on his campaign's Facebook page. "We can also confirm that no personal data was breached and our system remains secure". Kemp has countered that he is following the law and that Abrams and advocacy groups are trying to help noncitizens and others cast ballots illegally. The AP also reported that through a process Kemp calls "voter roll maintenance", his office has "cancelled over 1.4 million voter registrations since 2012" and that "nearly 670,000 registrations were cancelled in 2017 alone".
"This political stunt from Kemp just days before the election is yet another example of why he can not be trusted and should not be overseeing an election in which he is also a candidate for governor", the state party's executive director, Rebecca DeHart, said in a statement. "I don't use that term lightly. He made up a story like a 6-year-old trying to cover his tracks".
The racist ploy was in response to Oprah actively campaigning for Abrams in Georgia.