CNN

Former national security adviser Susan Rice fired back at President Trump's claim that the Obama administration should have properly vetted Trump's former national security adviser Michael Flynn.

"That's rich," Rice told CNN's Fareed Zakaria when she was asked to respond on Sunday.

"Let me explain how this process works. First of all, a former military officer such as General Flynn, who wants to retain his security clearance, would go through a process with his home agency, in this case the Defense Intelligence Agency, to have his clearance reviewed and renewed," Rice said, adding that clearance renewal happens at a "very routine level, never at a political level."

She continued: "But that's a very separate thing — the renewal of a clearance — from the vetting that goes into the appointment of any senior White House official, or any senior administration official. The Trump administration, like it’s — every previous administration, had an expectation and an obligation to vet, to their satisfaction, those individuals that the President was appointing to high positions, which is a separate and much more elaborate process than a security clearance."

The Trump administration has, in recent days, pointed a finger at former president Obama and his staff for not thoroughly investigating Flynn and his past communications with Russian officials. Trump doubled down on that assessement during an interview with CBS' John Dickerson on "Face the Nation," which aired Sunday morning.

Referring to Flynn, Trump said, "I didn't realize this, when he went to Russia, it was 2015 and he was on the Obama clearance. When General Flynn came to us, as you now know, he already had the highest clearance you can have."

He added: "I think the same clearance as the president of the United States would have. He had this really high clearance. And, by the way, they're so devastated because this only came up two days ago."

National Security Adviser Michael Flynn, arrives for the President Donald Trump, Japanese Prime Minister Shinzo Abe joint new conference in the East Room of the White House, in Washington, Friday, Feb. 10, 2017. AP Photo/Carolyn Kaster

Trump was likely referring to the House Oversight Committee's revelations earlier in the week that Flynn did not disclose payments he received from state-run media company Russia Today when he had his security clearance renewed in January 2016.

The Trump administration has also said that what Flynn did between the time when he retired from heading up the Defense Intelligene Agency in 2014 and when he was hired as national security adviser by Trump was not its concern.

When Flynn ultimately resigned from his position in February after it emerged that he had misled Vice President Mike Pence about conversations he'd had with Russian ambassador Sergey Kislyak, Trump said he felt for Flynn and that he had been treated horribly.

When asked whether he stood by those comments during an interview on Fox News on Friday, Trump said that while he did still feel badly, "Flynn "was approved by the Obama administration at the highest level."

"And when they say we didn’t vet, well Obama I guess didn’t vet, because he was approved at the highest level of security by the Obama administration," Trump said. "So when he came into our administration, for a short period of time, he came in, he was already approved by the Obama administration and he had years left on that approval."

Rice continued to fire back at Trump's claims on CNN, reiterating that the vetting process for a high-level national security post in the White House is a deeper check than the one required for security clearance renewal. "It gets into the financial information. It gets into your relationships and contacts. It gets into your behavior. It's a much deeper vet than what is done solely for the purpose of a security clearance," she said.