He called the hacks a "wake-up call", and said that the onus is now on states and the federal government to prevent a repeat in this year's midterms.
There is no evidence that Russian Federation tampered with any voting rolls in the 2016 election, federal officials say.
Head of cyber security at the Department of Homeland Security - Jeanette Manfra - said a "small number" of the 21 states targeted in the efforts were compromised.
"It's problematic that a foreign nation is involved in our election system because democracy is only as good as the people trust in results", Bush said, according to The Independent.
The targeting was part of a broader effort by Moscow to meddle in the presidential election, according to the USA intelligence community.
The revelations have sparked widespread fears that Russian Federation or another foreign government could try to interfere in future elections using cyberattacks and other tactics.
Summary: The head of cybersecurity at the Department of Homeland Security confirms that Russian Federation penetrated the US voter systems. There is however no evidence that the hackers managed to actually alter the rolls in any way, she added. Alarmingly, it seems that even when US officials are aware of such threats, intelligence agencies have been unable to effectively raise red flags.
Jeh Johnson, who served as the department's secretary during the hacking, said they were "able to determine that the scanning and probing of voter registration databases was coming from the Russian government".
When asked whether the U.S. was better prepared to thwart such attacks, Tillerson replied that if Russian Federation intends to interfere, "they're going to find ways to do that".
"I think it's important we just continue to say to Russia, 'Look, you think we don't see what you're doing". "'If you don't, you're going to just continue to invite consequences for yourself'".