Senators of both parties voiced support Tuesday for Senate Intelligence Committee Chairman Dianne Feinstein (D-Calif.) decision to publicly accuse the CIA of violating federal law and interfering with a committee investigation into the agency's interrogation practices, while some Republicans on the panel suggested that Democrats might also be at fault.

Just hours after the speech, Sen. Lindsey O. Graham (R-S.C.) suggested that "If what they're saying is true about the CIA, this is Richard Nixon stuff." He said he didn't know the details of the investigation and expected to be briefed soon. "The legislative branch should declare war on the CIA -- if it's true,"  he added.

But the two most-senior Republicans on the Intelligence Committee, Sens. Saxby Chambliss (R-Ga.) and Richard Burr (R-N.C.), declined to discuss the specifics of Feinstein's allegations. Chambliss rushed away from reporters after a midday vote.

Burr, a longtime member of both the House and Senate intelligence panels, said he hadn't yet read Feinstein's remarks but said he personally opposes openly discussing activities of the panel or the CIA.

Sen. Lindsey Graham (R-South Carolina) says Sen. Dianne Feinstein's (D-Calif.) claims that the CIA has searched Intelligence Committee computers are incredibly serious and "unnerved" him. (The Washington Post)

"I personally don’t believe that anything that goes on in the intelligence committee should ever be discussed publicly," he told reporters. "Certainly classified information, it’s breaking the law to discuss that. If I had my way, with the exception of nominees, there would never be a public intelligence hearing."

With Chambliss retiring after this year, Burr is next in line to serve as the top Republican on the panel or as its chairman, if the GOP retakes control of the Senate in November.

When pressed again to respond, Burr stood firm, saying that while not all agency activities are classified, "many of them are classified, and I believe that when [White House press secretary] Jay Carney gets up and talks about drone strikes, he has in fact talked about classified, covert operations and ought to be removed."

Sen. Marco Rubio (R-Fla.), a more junior member of the committee, said in an interview with Bloomberg TV that that situation "is a bit more complicated than what's being put out there by Senator Feinstein or others." Rubio called for an "impartial investigation" of the situation.

"I think until that point people should reserve judgment," he added. "But I would just caution that I don't think anyone has a clean hand and I think it's important for the full truth to come out.  I think people may be surprised to learn that, in this case, there were no good guys and maybe two or three bad ones."

Other Republicans with less direct knowledge of the situation expressed concerns and initial support for Feinstein. Sen. John McCain (R-Ariz.), a senior member of the Armed Services and Foreign Relations committees, called her allegations "very disturbing," adding: "We may need some kind of independent investigation." But McCain stressed that it is too soon to know whether federal law was broken. If the allegations are true, McCain said, there should be repercussions for the CIA and its director, John Brennan.

But in an interview Tuesday morning with NBC's Andrea Mitchell, Brennan denied Feinstein's allegations, saying "nothing could be further from the truth." He added that if he's done anything wrong, it will be President Obama to ask for his resignation.

Democrats, including some on the committee who frequently raise concerns with intelligence matters, praised Feinstein for speaking out. During their weekly caucus luncheon, she received two standing ovations. First, when Majority Leader Harry M. Reid (D-Nev.) mentioned her speech and again when she urged her colleagues to read her remarks, according to a senior aide familiar with the meeting but not authorized to speak publicly about it.

Sen. Patrick J. Leahy (D-Vt.), the chamber's longest-serving Democrat, told reporters that "in 40 years here, it was one of the best speeches I’d ever heard and one of the most important."

Sen. Ron Wyden (D-Ore.) said that her speech "goes precisely to the question of whether the Congress can do effective oversight over the modern intelligence apparatus." He noted that at the recent annual public hearing on worldwide threats, he asked whether federal laws barring snooping on computers applied to the CIA. He said that the agency has replied in writing that such laws do apply to agency officials.

Sen. Mark Udall (D-Colo.), another outspoken member of the panel, said Feinstein's concerns bolster his own attempts to get answers about the CIA's interrogation program. "Unfortunately, the CIA responded by trying to hide the truth from the American people about this program and undermine the Senate Intelligence Committee's oversight role by illegally searching committee computers," he said in a statement. "The U.S. Constitution is clear and Coloradans agree: The separation of powers and aggressive oversight are fundamental to our democracy, and Coloradans can count on me to continue to protect these foundational pillars no matter who is in the White House."

And Sen. Martin Heinrich (D-N.M.) also praised Feinstein's decision to go public. "I know she has tried to address this discretely through a constructive dialogue with the administration, but a steady stream of inaccurate and off-the-record anonymous leaks to the press have made that effort impossible," he said in a statement.

Senate Intelligence Chair Dianne Feinstein (D-Calif.) accused the CIA of breaking the law by searching her committee's computers. The Post's Karen Tumulty, Scott Wilson, Terence Samuel and Adam Goldman explain the impact in Washington. (Julie Percha and Theresa Poulson/The Washington Post)