As Republicans sought to steer public attention to unproven claims that Barack Obama's administration spied on Trump, Rice said that her final months in the White House were focused on Russia's interference in the election that brought Trump to power.
"The allegation is that somehow Obama administration officials utilized intelligence for political purposes. That's absolutely false," she told MSNBC television.
Early Tuesday, Trump retweeted a report alleging Rice had ordered the compilation of "spreadsheets" detailing phone conversations between Trump associates and foreign officials intercepted by US intelligence agencies.
On Monday, two reports claimed that Rice, who was Obama's top national security aide, had helped reveal the identities of Trump officials whose communications were swept up in regular US spying on foreign targets.
While the reports cited no supporting evidence, Trump backers pointed to them to support the president's allegations that the Obama administration used US intelligence bodies to spy on him.
Rice said Obama had ordered an extensive investigation on how Russia disrupted the 2016 election. She conceded that that could have resulted in Trump officials' communications being picked up and read by US intelligence.
"From basically August through the end of the administration (January 20) we were hearing more and more, getting more and more information about Russian interference in our electoral process. It was of grave concern," she said.
US President Donald Trump. Source: AAP
"There was a pace of reporting that accelerated as the intelligence community got more and more information on that."
Trump and his Republican supporters want FBI and Congressional investigations to target claims that Obama spied on his successor, rather than Moscow's interference in the election.
Trump has repeatedly called the Russian issue "fake news," and on Sunday made a plea to "find the leakers." His spokesman Sean Spicer complained Monday that US media was, in its focus on the Russia issue, pursuing the wrong story.
Devin Nunes, chairman of the House Intelligence Committee probing the Russia scandal, has tried to direct attention to how the Obama administration used intelligence reports.
But Rice and Democrats say the key issue is still what Russia did and whether there was any collusion with the Trump team.
"Right now, there's a cloud swirling over the White House," said Eric Swalwell, a Democratic member of Nunes's panel. "We will not stop until we find out what happened."
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