"I think it was personal. He likes to intimidate," Rice said of his possible reasons for interfering. She called him "an eye-for-an-eye kind of person."
"Now he's saying, 'I'm going to question the legitimacy of your election by hacking into it' and so forth," Rice said.
Rice urged Americans not to be rattled by Putin's actions.
"Don't let him get the satisfaction of thinking we don't believe our own elections to be legitimate," she said.
"What you can't do is be intimidated by Putin or let him play these psychological games," Rice added. "I'm not going to question the legitimacy of their vote because Vladimir Putin tried to interfere in the elections. Let's trust our fellow citizens to have been smart enough to vote for the people they thought they ought to be voting for."
Rice weighed in on warnings that then-President Barack Obama and others in his administration gave Donald Trump about his choice for national security adviser, Michael Flynn, and Flynn's ties to Russia.
Flynn was fired after his ties to Russian officials came to light. Rice said Americans should be "comforted" by Trump's choice to replace him.
"As a matter of principle, you can talk to anybody in that period, but you should never suggest that you might be making policy and maybe they should just wait until there's a change in administration. The principle is you wouldn't do that," Rice said.