Republican lawmakers on Sunday sought to temper the impact of the latest bombshell reports involving President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE and Russia, while their Democratic colleagues renewed calls to protect special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE's investigation.

The responses came after both The New York Times and The Washington Post reported new details over the weekend involving allegations of Trump's close ties with Moscow, sparking renewed concerns about the fate of Mueller's probe.

Sen. Ted Cruz Rafael (Ted) Edward CruzLoeffler calls for hearing in wake of Netflix's 'Cuties' Health care in the crosshairs with new Trump Supreme Court list 'Parks and Rec' cast members hosting special reunion to raise money for Wisconsin Democrats MORE (R-Texas), a member of the Senate Judiciary Committee, on NBC criticized Washington, D.C.'s, focus on the Mueller investigation as out of touch with the rest of the country.

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And Sen. Lindsey Graham Lindsey Olin GrahamThe Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters Senate Democrats' campaign arm announces seven-figure investment to boost Graham challenger Graham: Comey to testify about FBI's Russia probe, Mueller declined invitation MORE (R-S.C.), a close ally of the president, raised doubts about some of the reporting's accuracy.

The New York Times reported Friday that the FBI was so concerned about Trump’s firing of former bureau chief James Comey James Brien ComeyTrump jabs at FBI director over testimony on Russia, antifa Graham: Comey to testify about FBI's Russia probe, Mueller declined invitation Barr criticizes DOJ in speech declaring all agency power 'is invested in the attorney general' MORE that it opened an inquiry into whether the president was working on behalf of Russian interests.

And The Washington Post reported on Saturday that Trump has kept details of his meetings with Russian President Vladimir Putin from top officials in his administration, including withholding notes from an interpreter.

The White House dismissed the reports as “inaccurate” and defended Trump’s record on Russia, while the president called the stories “insulting” and “ridiculous.”

Secretary of State Mike Pompeo Michael (Mike) Richard PompeoHillicon Valley: FBI chief says Russia is trying to interfere in election to undermine Biden | Treasury Dept. sanctions Iranian government-backed hackers Treasury Dept. sanctions Iranian government-backed hackers The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE would not directly address The New York Times story, but in a Sunday interview called it "ludicrous" to consider Trump a national security threat.

Both parties on Sunday called for a closer look at Trump’s behavior toward Russia, with Democrats and Republicans both saying Trump's actions speak for themselves. However, Democrats argue that Trump has been soft on Russia while Republicans believe the opposite.

Multiple GOP guests appearing on the Sunday show circuit pointed to the Trump administration’s track record of levying sanctions against Moscow and expelling a number of Russian diplomats from the U.S. as evidence the president is tough on Russia.

Graham on “Fox News Sunday” expressed skepticism with the accuracy of the Times report and suggested it provided more proof of bias at the FBI than evidence against Trump.

"I, for one, don’t trust what I read in The New York Times," he said, but added "if this really did happen, Congress needs to know about it."

Cruz said he would consider any corroborated allegations that emerge, but called it "premature" to attempt to subpoena notes of the president's meetings with Putin.

House Minority Leader Kevin McCarthy Kevin Owen McCarthyTrump's sharp words put CDC director on hot seat House GOP leader says he trusts Trump over CDC director on vaccine timing The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump contradicts CDC director on vaccine, masks MORE (R-Calif.) defended Trump's right to keep private the details of his meetings with Putin, suggesting on CBS's "Face the Nation" that doing so was part of the president's strategy to build a relationship with a foreign leader.

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"I know this administration. I know this Congress is very tough on Russia, and we will continue to be so," he said. "But I want this president to be able to build a relationship, even on a personal level with all the world leaders as well."

However, Democrats on Sunday highlighted the president's call during the 2016 campaign for Russia to hack Hillary Clinton Hillary Diane Rodham ClintonHillicon Valley: FBI chief says Russia is trying to interfere in election to undermine Biden | Treasury Dept. sanctions Iranian government-backed hackers The Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters FBI chief says Russia is trying to interfere in election to undermine Biden MORE's emails; his public skepticism over the U.S. intelligence community's assessment that Russia meddled in the 2016 election; and his performance at a joint press conference with Putin last year in Helsinki.

“The right answer is … to protect the Mueller investigation at all costs, let it get to its end, make sure that the results are made public,” Sen. Tim Kaine Timothy (Tim) Michael KaineBiden promises Democratic senators help in battleground states Second GOP senator to quarantine after exposure to coronavirus The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Va.) said on “Meet the Press.”

Sen. Mark Warner Mark Robert WarnerIntelligence chief says Congress will get some in-person election security briefings Overnight Defense: Trump hosts Israel, UAE, Bahrain for historic signing l Air Force reveals it secretly built and flew new fighter jet l Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' House approves bill to secure internet-connected federal devices against cyber threats MORE (D-Va.), the ranking member of the Senate Intelligence Committee, said on CNN that whether Trump ever worked on behalf of the Russians is "the defining question" of Mueller's investigation.

Sen. Christopher Coons Christopher (Chris) Andrew CoonsBiden promises Democratic senators help in battleground states Shakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Del.) on Fox News maintained that the latest reports underscore the need to allow Mueller's investigation to reach "its logical conclusion."

The chairmen of the House Foreign Relations, Judiciary and Intelligence committees have all said in the wake of this weekend's reports that they will look into Trump's relationship with Russia.

House Foreign Affairs Committee Chairman Rep. Eliot Engel Eliot Lance EngelThe Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep Coons beats back progressive Senate primary challenger in Delaware Overnight Defense: Trump hosts Israel, UAE, Bahrain for historic signing l Air Force reveals it secretly built and flew new fighter jet l Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' MORE (D-N.Y.) responded Saturday to the Post story with a pledge for upcoming hearings.

We will be holding hearings on the mysteries swirling around Trump’s bizarre relationship with Putin and his cronies, and how those dark dealings affect our national security. — Eliot Engel (@RepEliotEngel) January 13, 2019

The future of the Mueller investigation, which has thus far implicated five former Trump associates and more than 20 Russian nationals, is also sure to be front-and-center at this week's confirmation hearings for attorney general nominee William Barr.

Democrats have uniformly said they'd like guarantees from Barr that he will not allow interference in Mueller's investigation.

"I mean, clearly he’s a good lawyer. No question," Sen. Dick Durbin Richard (Dick) Joseph DurbinMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled Senate Republicans signal openness to working with Biden Top GOP senator calls for Biden to release list of possible Supreme Court picks MORE (D-Ill.), a member of the Senate Judiciary Committee, said on "This Week."

"But when it comes to this delicate political situation, the power of the presidency, whether this investigation is warranted, Bill Barr had better give us some ironclad, rock-bottom assurances in terms of his independence and his willingness to step back and let Mueller finish his job," Durbin said.