Lawmakers are vying to get the first crack at questioning Donald Trump Jr. about his meeting with a Russian lawyer offering compromising information on Hillary Clinton Hillary Diane Rodham ClintonJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Momentum growing among Republicans for Supreme Court vote before Election Day Warning signs flash for Lindsey Graham in South Carolina MORE .

The Senate Intelligence, Senate Judiciary and House Intelligence committees are conducting separate investigations into Russia’s interference in the 2016 election, including potential ties between Trump campaign officials and Moscow.

But Tuesday’s political bombshell that Trump Jr. was told the “very high level and sensitive information … is part of Russia and its government's support for Mr. Trump,” is threatening to reignite a turf battle, with lawmakers publicly vying to get President Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE’s eldest son to talk with their committees about his 2016 meeting.

Senate Judiciary Committee ranking member Dianne Feinstein (D-Calif.) argued Tuesday that Trump Jr. should testify publicly before her panel, saying the meeting in question is "very much our committee business."

"This is aired on front page newspapers. It should be aired front page [in the] United States Senate. The committee of jurisdiction is clearly the Judiciary Committee," she told reporters. “It’s not an Intelligence matter.”

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Feinstein, who is also a member of the Senate Intelligence Committee, added that she wants to make progress on the issue as soon as Tuesday and has "urged the chairman to move quickly" to bring Trump Jr. in to talk.

A spokesman for Sen. Chuck Grassley, the chairman of the Judiciary Committee, didn't respond to a request for comment. But the Iowa Republican separately defended Trump Jr., praising him for being willing to testify and for his “transparency.”

Judiciary Committee member Lindsey Graham (R-S.C.) backed up Feinstein, saying their committee "has jurisdiction over here."

"If you're ever approached about getting help from a foreign government the answer is no," he said. "I think we need to hear from Donald Trump Jr., yeah I do."

Graham, one of the Senate’s most vocal Russia hawks, was one of the few Republicans who openly criticized Trump Jr. on Capitol Hill on Tuesday — even as many of his GOP colleagues went on defense or dodged the issue altogether.

The Judiciary Committee, which has oversight of the FBI, is one of five committees investigating Russia's election interference, in addition to the Department of Justice-FBI probe led by special counsel Robert Mueller.

But the Judiciary panel could find itself in a battle with the Senate Intelligence Committee’s separate investigation.

That probe has increasingly moved into the spotlight amid closed-door meetings with top administration officials, and is widely viewed as Congress’s best chance at getting to the bottom of Russia’s election interference.

Senate Minority Leader Charles Schumer Chuck SchumerVideo of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Graham signals support for confirming a Supreme Court nominee this year Pelosi orders Capitol flags at half-staff to honor Ginsburg MORE (D-N.Y.) threw his support behind both committees on Tuesday, while Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMomentum growing among Republicans for Supreme Court vote before Election Day Trump expects to nominate woman to replace Ginsburg next week Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral MORE (R-Ky.) said the Intelligence Committee has “ball control.”

“What I have a lot of confidence in is the Intelligence Committee handling this whole investigation. Senator [Richard] Burr [R-N.C.] and Senator [Mark] Warner [D-Va.] have ball control, and we'll hear from them later,” he told reporters when asked about Trump Jr.

Sen. John Cornyn John CornynCalls grow for Biden to expand election map in final sprint Bipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection MORE (Texas), the No. 2 Senate Republican, also backed the idea of Trump Jr. testifying before the Intelligence Committee.

Cornyn, like Feinstein, is a member of the Judiciary and Intelligence committees.

Intelligence Chairman Burr remained tight-lipped on Tuesday about whether he would request that Trump Jr. meet with his panel, but pushed back against it the idea of it being a Judiciary Committee matter.

"I don't see how it could be [Judiciary jurisdiction], but she's ranking member of the Judiciary Committee, so I imagine she wants to claim as much jurisdiction as she can," he told reporters when asked about Feinstein's comments.

Multiple Republicans on the Intelligence Committee, including moderate Sen. Susan Collins Susan Margaret CollinsJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally Momentum growing among Republicans for Supreme Court vote before Election Day MORE (R-Maine), have backed the idea of Trump Jr. meeting with them as part of their investigation.

Warner said "of course" his panel should hear from Trump Jr., but appeared open to him also talking to the Judiciary Committee.

"This was part of a Russian government effort to discredit Clinton and help Trump. So all of these denials that we have heard ... they're all patently false," he said. "It makes the [Intelligence Committee] investigation all that more important."

It isn’t be the first time Senate committees have bumped jurisdictional elbows. GOP senators mulled widening the Russia probe earlier this year, but backed away after leadership signaled that the Intelligence Committee could handle the investigation.

The Intel and Judiciary committees both met with Mueller and both requested former FBI Director James Comey meet with them in the wake of his firing. Comey declined the Judiciary Committee's invite and testified publicly before the Senate Intelligence Committee.

The move appeared to frustrate Grassley and Feinstein, and there’s little sign that Judiciary Committee members are willing to back down.

A subcommittee overseen by Graham and Sen. Sheldon Whitehouse Sheldon WhitehouseLWCF modernization: Restoring the promise Restaurant owner defends calamari as 'bipartisan' after Democratic convention appearance Warren calls on McConnell to bring Senate back to address Postal Service MORE (D-R.I.) held a hearing Tuesday on how to avoid running into Mueller’s jurisdiction.

Whitehouse said the panel had faith in Mueller, but it also has “has a duty” to dig into Russia’s election interference.

“These questions are deadly serious, as they implicate the President’s fitness to perform his duties,” he said. “I hope the full committee get’s energized.”

Charles Tiefer, a professor at the University of Baltimore School of Law, told lawmakers during Tuesday’s hearing to not “give your job and your turf away to Intel” — earning a laugh from Graham.

Further complicating the battle for Trump Jr.’s time, Rep. Adam Schiff (Calif.), the top Democrat on the House Intelligence Committee, also wants him to testify.

"These participants are all going to have to come before the committee," Schiff told MSNBC. "We're going to have to try to obtain any relevant emails and documents."

Trump Jr. has indicated he will cooperate with congressional investigators and hasn't specifically ruled out appearing before multiple panels.

He also tweeted Tuesday an email chain of his conversations setting up the meeting in question — a move that only increased scrutiny from lawmakers.

The information offered by a Russian lawyer “would incriminate Hillary and her dealings with Russia and would be very useful to your father,” reads one of the emails from Rob Goldstone, who acted as an intermediary to set up the meeting.

“This is obviously very high level and sensitive information but is part of Russia and its government's support for Mr. Trump,” he continued.

Updated 5:42 p.m.

Katie Bo Williams contributed.