Graham's comments come one day after his panel heard testimony from former acting Attorney General Sally Yates, who detailed the steps she took to warn the White House that former national security adviser Michael Flynn was vulnerable to blackmail by the Russian government.
Sen. Chuck Grassley (R-Iowa) on Monday asked both Yates and former Director of National Intelligence James Clapper if they have ever been quoted anonymously in news reports - or authorized someone else to be quoted anonymously in news reports - about matters relating to Trump, his associates, or Russian meddling.
After the hearing, Mr Trump tweeted: "The Russia-Trump collusion story is a total hoax, when will this taxpayer funded charade end?"
Trump said in a press conference three days after Flynn resigned, however, that when he looked at the information provided to him about Flynn's conversations with Kislyak, "I said, 'I don't think he did anything wrong". But she noted that "you should not draw from that an assumption that that means that the answer is yes". The Senate Judiciary Committee is also probing potential links between Russian agents and people linked to the President's campaign.More news: Construction costs increasing with tariff on Canadian softwood
Further, said Klobuchar, the Trump administration chose to keep Flynn on an additional 18 days after Yates' warning, "and in fact, two days after having this warning allowed him to sit in on an hour-long telephone call between the president of the United States and [Russian President] Vladimir Putin". The Russians can use compromise material and information in a variety of ways, sometimes overtly and sometimes subtly ... our concern was that you have a very sensitive position like the National Security Adviser, and you don't want that person to be in a position where, again, the Russians have leverage over him.
"I don't know if we need to subpoena her", Graham said of Rice.
Flynn, who was sacked from his White House position after lying about December phone calls he had with Russian Ambassador Sergey Kislyak, is under investigation in Congress, the FBI and the Pentagon over his dealings with Russians dating back to late 2005. Pence said in January that Flynn denied those calls involved sanctions placed on Russian Federation by the Obama administration in response to its election meddling.
It's yet the latest bit of evidence of an ongoing feud between the past and present presidential administrations as well as the tension between Trump's inner circle and the United States intelligence community.More news: Ron Wyden questions Attorney General Jeff Sessions' 'fitness for office'
On Monday, Trump posted a tweet that had a simple message: "I'm innocent".
Trump's executive order, which banned Syrian refugees from entering the USA as well as people from seven Muslim-majority countries, caused chaos at airports and drew protests around the country.
"They are attuned, it seems, more to defending the president than to taking care of national security business in an appropriate way", Whitehouse said.
The dual testimony by Yates and Clapper returned the spotlight to the simmering controversy over Russia's meddling in last year's US election.More news: EBRD Bank sees oil price rebound boosting economic growth
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