Top Senate Republicans said Tuesday the Intelligence Committee should investigate the circumstances surrounding the resignation of Michael Flynn as President Trump’s national security adviser and ask him to appear before Congress for questioning.

GOP lawmakers stopped short of calling for an independent committee to look into Flynn’s actions. The creation of such a panel, demanded by Democrats, would elevate the investigation and allow for televised, public hearings.

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But Republicans largely agreed the Flynn matter should be included in a current Intelligence Committee probe into Russian interference in the U.S. presidential election.

“It’s likely that General Flynn will be, at some point, asked to come and talk to the committee about both post-election activities and any other activities he would be aware of,” said Sen. Roy Blunt Roy Dean BluntOn The Money: Trump undercuts GOP, calls for bigger COVID-19 relief package | Communities of color hit hardest financially by COVID-19 | Businesses, states pass on Trump payroll tax deferral Trump undercuts GOP, calls for bigger COVID-19 relief package Businesses, states pass on Trump payroll tax deferral MORE (R-Mo.), a member of Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellSenate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll The Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally MORE’s (R-Ky.) leadership team who serves on the Intelligence panel.

McConnell added it’s “highly likely” the Intelligence panel will investigate Flynn.

Across the Capitol, House GOP leaders charged with oversight were less aggressive than their Senate counterparts, seeming to shrug off calls for Congress to get more involved.

The controversy with Flynn began after reports surfaced that he had privately discussed Obama-initiated sanctions with Russia’s ambassador to the U.S. before Trump took office and then misled Vice President Pence and other top Trump administration officials about the matter.

House Oversight Committee Chairman Jason Chaffetz Jason ChaffetzThe myth of the conservative bestseller Elijah Cummings, Democratic chairman and powerful Trump critic, dies at 68 House Oversight panel demands DeVos turn over personal email records MORE (R-Utah) deferred to his chamber’s Intelligence Committee, which has been conducting a broad review of Russia’s attempts to influence the elections. That probe includes campaign communications with the Russian government.

“I think that situation has taken care of itself. I know that the intel committee is looking into the hacking issue,” Chaffetz told reporters. “It’s not something the Oversight Committee can actually look at because sources and methods are the exclusive purview of the intel committee.”

House Intelligence Committee Chairman Devin Nunes (R-Calif.), a member of Trump’s transition team, said his panel would instead review the intelligence community leaks of Flynn’s phone calls with the Russian ambassador, CNN reported.

Nunes spokesman Jack Langer said the committee “will continue to investigate any intelligence our counterintelligence issues involving Russia and follow the facts wherever they lead.”

Speaker Paul Ryan Paul Davis RyanAt indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates Peterson faces fight of his career in deep-red Minnesota district MORE (R-Wis.) offered support for the decision to accept Flynn’s resignation but didn’t push for action from the House.

“I’m not going to prejudge the circumstances surrounding this. I think the administration will explain the circumstances that led to this,” he told reporters.

Democrats, still smarting over losing the White House to Trump, said the Flynn episode raises broader concerns about the Trump team’s ties to Russia.

“There are so many questions that have to be answered. I think we need the sworn testimony of Michael Flynn, we need sworn testimony of [former Trump campaign chairman] Paul Manafort, we need sworn testimony from people in the White House who knew this for over a month and had done nothing,” Sen. Claire McCaskill Claire Conner McCaskillDemocratic-linked group runs ads in Kansas GOP Senate primary Trump mocked for low attendance at rally Missouri county issues travel advisory for Lake of the Ozarks after Memorial Day parties MORE (D-Mo.), who serves on both the Armed Services and Homeland Security committees, told The Hill.

Flynn, a retired Army lieutenant general, submitted his resignation hours after The Washington Post reported that the acting attorney general had warned top White House officials last month that Flynn could be blackmailed by Russia because he was deliberately mischaracterizing his discussions with Russian Ambassador Sergey Kislyak. FBI agents interviewed Flynn just days after Trump’s inauguration, The New York Times reported on Tuesday.

The White House insisted Tuesday that Flynn had not broken any laws. Press secretary Sean Spicer said that Trump fired Flynn because his trust in him had “eroded,” rather than taking issue with his calls to the Russian ambassador.

Democrats signaled their desire to keep the pressure on the GOP.

“I just think it’s, frankly, outrageous that Republicans are standing mute. … This is certainly a bigger threat to national security than Hillary Clinton Hillary Diane Rodham ClintonBarr criticizes DOJ in speech declaring all agency power 'is invested in the attorney general' Virginia Democrat blasts Trump's 'appalling' remark about COVID-19 deaths in 'blue states' The Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally MORE’s private email server,” McCaskill said.

Kurt Bardella, a prominent Trump critic who worked for former House Oversight Committee Chairman Darrell Issa (R-Calif.), accused Chaffetz of showing a double standard with the Trump administration.

“If the first month of the Obama administration had been like it has during the Trump administration, the Oversight Committee would have been issuing subpoenas, launching investigations and convening hearings at a record pace,” Bardella said.

One House Republican who didn’t want to be identified said he’d like to hear directly from Trump about what he knew and when he knew it. Spicer said Trump “absolutely” did not direct Flynn to conduct back-channel communications with Russia while Obama was still in power.

Rep. Scott Perry (R-Pa.), a House Freedom Caucus member, said Republicans’ reluctance to judge the situation without knowing the full story could be easily remedied.

“We have to be careful because of commenting without the facts. But at the same time, I don’t know how you get the facts without doing some investigation,” Perry said.

Sen. Marco Rubio Marco Antonio RubioHillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Intelligence chief says Congress will get some in-person election security briefings Republican Senators raise concerns over Oracle-TikTok deal MORE (R-Fla.), whom Trump defeated in the GOP presidential primaries, said he wants to see more evidence before bringing Flynn before Congress. But the senator said he was certain the committee’s existing Russia investigation would now include Flynn.

“I have full confidence that the intel committee is going to do a good job,” Rubio told The Hill. “And if we don’t, then I will let everyone know that we didn’t.”

Jordain Carney and Alexander Bolton contributed.