A long-simmering dispute between U.S. senators and the CIA flared on Tuesday as a top-ranking lawmaker publicly accused the agency of snooping on congressional staffers -- and another said that if the allegations are true, Congress "should declare war on the CIA."

Sen. Dianne Feinstein, D-Calif., aired the details of the formerly quiet controversy in a scathing address on the Senate floor on Tuesday morning. She said the agency may have committed a crime by improperly searching a computer network established for Congress as part of its investigation into allegations of CIA abuse in a Bush-era detention and interrogation program.

She also confirmed that the matter has been referred to the Justice Department by the CIA inspector general.

"Based on what Director [John] Brennan has informed us, I have grave concerns that the CIA search may well have violated the separation of powers principles embodied in the United States Constitution including the Speech and Debate clause," she said. "It may have undermined the constitutional framework essential to effective congressional oversight of intelligence activities or any other government function."

Brennan, speaking at a separate event shortly afterward, denied the allegations. "Nothing can be further [from] the truth, we wouldn't do that," he said.

Both Feinstein and the CIA have accused each other's staffs of improper behavior. Brennan, asked about Feinstein's accusations, said the agency was not trying to stop the committee's report and that it had not been spying on the panel or the Senate. He said the appropriate authorities would look at the matter further and "I defer to them to determine whether or not there was any violation of law or principle."

But other senators jumped into the fray after Feinstein delivered her floor speech.

"Heads should roll, people should go to jail if it's true," Sen. Lindsey Graham, R-S.C., said. "If it is, the legislative branch should declare war on the CIA."

The White House, meanwhile, declined to referee. Press Secretary Jay Carney would not take sides when asked about the conflict at Tuesday's press briefing. He said President Obama supports the committee's investigation, but the issue at hand is "under review" by the inspector general. "So I'm not going to get into the specifics about allegations," he said.

The controversy stems from an agreement between the committee and the agency to allow committee aides to review millions of sensitive documents at a CIA-leased secure location in northern Virginia.

The CIA allowed the committee to use a search tool to comb through the material -- in doing so, Feinstein said staffers came across an internal review of the agency's practices. She stressed that staffers did not hack into the network to obtain it. At this point, she claims, the CIA searched the network -- including the committee's internal network -- and removed the documents.

"The CIA did not ask the committee or its staff if the committee had access to the internal review or how we obtained it. Instead, the CIA just went and searched the committee's computers. The CIA has still not asked the committee any questions about how the committee acquired" the review, she said.

News reports last week first revealed the allegations against the CIA. In response, Senate Armed Services Committee Chairman Carl Levin, D-Mich., said the alleged spying, if true, "would be an extremely serious matter" and could "violate federal law."

But Brennan has pushed back on the speculation. He said last week he was "deeply dismayed" that some Senate members made allegations that "are wholly unsupported by the facts."

"I am very confident that the appropriate authorities reviewing this matter will determine where wrongdoing, if any, occurred in either the executive branch or legislative branch," Brennan said in a statement. "Until then, I would encourage others to refrain from outbursts that do a disservice to the important relationship that needs to be maintained between intelligence officials and Congressional overseers."

Fox News' Kara Rowland and The Associated Press contributed to this report.