Former national security adviser Michael Flynn on Monday reportedly declined to cooperate with a Senate subpoena, setting up a potential showdown between Congress and the administration over a key witness in the investigation into Russian interference in the presidential election.

Flynn for months has said he would testify before Congress only if granted immunity, a deal lawmakers have shied away from making to avoid interference with a separate, federal probe.

Senate leaders now must decide how far to go in enforcing the subpoena, issued for documents in the Senate Intelligence Committee investigation.

If they do seek to enforce the subpoena, they will need the cooperation of the Justice Department. And it’s unclear which official would be responsible for handling the referral.

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For now, the Senate panel’s appetite to hold Flynn in contempt — the first step to enforcing the subpoena — appears limited. Senate Intelligence Committee Chairman Richard Burr Richard Mauze BurrRep. Mark Walker says he's been contacted about Liberty University vacancy Overnight Defense: Trump rejects major cut to military health care | Senate report says Trump campaign's Russia contacts posed 'grave' threat Senate report describes closer ties between 2016 Trump campaign, Russia MORE (R-N.C.) last week declined to say whether he would take the step.

“I'm not going to go into what we might or might not do,” he told reporters. “We've got a full basket of things that we're willing to test.”

Pressed if senators would try to hold Flynn in contempt of Congress, Senate Majority Whip John Cornyn John CornynAirline job cuts loom in battleground states Senate 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 MORE (R-Texas) said, “No, the Fifth Amendment provides you an absolute right against self-incrimination. That's something he's entitled to do.”

Democrats also stopped short of calling for Flynn to be held in contempt.

Sen. Ron Wyden Ronald (Ron) Lee WydenGOP senator blocks Schumer resolution aimed at Biden probe as tensions run high Republican Senators raise concerns over Oracle-TikTok deal Hillicon Valley: TikTok, Oracle seek Trump's approval as clock winds down | Hackers arrested for allegedly defacing U.S. websites after death of Iranian general | 400K people register to vote on Snapchat MORE (D-Ore.) said that he would “go to the mat” to ensure the subpoena is enforced. But asked about holding Flynn in contempt, he deferred to Burr and ranking member 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.).

“I believe both the Intelligence and Judiciary Committees should continue to seek other ways to gain access to this information,” Senate Judiciary Committee ranking member Dianne Feinstein Dianne Emiel FeinsteinSenators offer disaster tax relief bill Democrats back away from quick reversal of Trump tax cuts Congress must save the Postal Service from collapse — our economy depends on it MORE (D-Calif.) said in a statement that called the refusal “unfortunate but not unexpected.”

Congressional investigations have a longstanding history of coordinating with any simultaneous federal probes to avoid inadvertently damaging the Justice Department’s ability to levy prosecutions in a given case.

In this case, the federal probe into Flynn appears to be escalating. The U.S. Attorney’s office in Northern Virginia reportedly issued its own subpoenas for records related to Flynn’s business earlier this month.

The appointment of a special counsel, former FBI Director Bob Mueller, may also remove some of the pressure on Senate leaders to go after Flynn. The move, intended to remove the specter of political interference in the investigation, was met with widespread support on Capitol Hill.

“Congress has tools at its disposal, but how it uses them is a strategic calculation,” former National Security Agency counsel Susan Hennessey and Harvard Law Review editor Helen Klein Murillo wrote on the national security blog Lawfare.

“How the Committee proceeds may depend both on how much cooperation it anticipates from the Department of Justice — which may depend in large part of whether the relevant official is Mueller or Rosenstein — and on its own calculation about the wisdom of forcing the issue given the newly appointed special counsel,” they write, referring to Deputy Attorney General Rod Rosenstein.

Democrats have previously expressed fears that the Justice Department would refuse to enforce any congressional subpoenas related to ties between President Trump's campaign and Russia.

There is a precedent to refuse.

The Senate certified a criminal contempt charge against Attorney General Eric Holder Eric Himpton HolderThe Hill's Campaign Report: Trump's rally risk | Biden ramps up legal team | Biden hits Trump over climate policy Biden campaign forming 'special litigation' team ahead of possible voting battle Pompeo, Engel poised for battle in contempt proceedings MORE during President Obama’s second term, but the U.S. attorney refused to bring it before the grand jury.

Typically, the full Senate certifies and issues a so-called contempt referral to the “appropriate United States attorney” — for sitting executive branch officials, often the U.S. attorney for the District of Columbia.

But Flynn is not a sitting U.S. official. And the scope of Mueller’s authority in the Russia probe — which includes “the full power and independent authority to exercise all investigative and prosecutorial functions of any United States Attorney” — has led national security law experts to question whether Rosenstein or Mueller would be responsible for enforcing the subpoena.

Attorney General Jeff Sessions Jefferson (Jeff) Beauregard SessionsTrump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status White House officials voted by show of hands on 2018 family separations: report MORE had previously stepped aside from the probe for failing to disclose a meeting with the Russian ambassador during his confirmation hearing.

Rosenstein had faced fierce scrutiny for his role in the dismissal of the man formerly in charge of the probe, then-FBI Director James Comey.

Trump has continued to back Flynn. He has previously applauded Flynn’s demands for immunity, citing a “witch hunt” against him.

Flynn, who was ousted in February for misleading Vice President Pence about the contents of a December phone call to the Russian ambassador, took tens of thousands of dollars in payments from the Russian state-backed network RT and failed to tell the government when he reapplied for his security clearance.

The former intelligence official invoked his Fifth Amendment right against self-incrimination, citing an “escalating public frenzy” surrounding the request.

“The context in which the Committee has called for General Flynn’s testimonial production of documents makes it clear that he has more than a reasonable apprehension that any testimony he provides could be used against him,” Flynn’s lawyers wrote in a letter to Burr and Warner, according to The Washington Post.

Jordain Carney contributed to this story.