According to Isikoff, the Arizona attack involved "malicious software that was introduced into its voter registration system but no successful exfiltration of data."
The attack in Illinois was more successful and the state had to shut down its system for a few days. Isikoff said the hackers downloaded information on at least 200,000 voters.
The FBI is warning state officials to boost their election security in light of evidence that hackers breached related data systems.
In a confidential "flash" alert from its cyber division, the FBI said it's investigating the incidents and advising states to scan their systems for specific signs of hacking.
The Aug. 18 warning came just days after Homeland Security Secretary Jeh Johnson hosted a call with secretaries of state and other state election officials to talk about cybersecurity and the election infrastructure.