The top Democrats on the Senate intelligence and judiciary panels are planning hearings to consider establishing new authorities for federal courts to oversee the use of armed drone strikes against suspected terror targets worldwide.
FISA established a special federal court to approve surveillance on suspected foreign spies working inside the United States.
Senate Judiciary chairman Sen. Pat Leahy (D-Vt.) and Ranking Member Sen. Chuck Grassley (R-Iowa) have also indicated "their concern and interest" in introducing some sort of FISA-like legal check on the administration's authority to execute armed drone strikes, the California Democrat said.
Feinstein noted that Sen. Dick Durbin (D-Ill.), who chair's the Judiciary committee's subpanel on the Constitution, Civil Rights and Human Rights subpanel is already planning to hold hearings on the issue.
Her comments came after Thursday's confirmation hearing for White House counterterrorism chief John Brennan to become the new head of Central Intelligence Agency.
"I know the [Senate] Judiciary committee is interested" in developing some kind of legal framework to govern the use of armed drones in counterterrorism operations, she said.
"This is now out in the public arena, and now it has to be addressed," Feinstein said.
The effort to open the armed drone program to a FISA-like court came after the unexpected release of a previously confidential Department of Justice white paper justifying U.S. drone operations — even if those strikes target American citizens.
If approved, the FISA-like authority for drone operations would allow lawmakers to directly address some of the perceived problems with the program, without dealing with the issues of classification surrounding the program.
"Right now it is very hard [to oversee] because it is regarded as a covert activity, so when you see something that is wrong and you ask to be able to address it, you are told no," due the program being steeped in secrecy.
"We know it exists and I think this [program] has gone as far as it can go, as a covert activity, and I think we really need to address it," Feinstein said.
That said, Feinstein made clear the system of analysis and verification in place at CIA and the White House to determine who ends up on the so called CIA "kill list" for a drone strike is "a solid process."
Officials from the Senate intelligence committee also have sent a team of observers to CIA headquarters in Langley, VA "on a regular basis" to review the intelligence analysis that goes into the process, according to Feinstein.
"The intelligence that is used [in the drone program] is very careful and very good," she said.
But within that process, there is an "absence of knowing who is responsible for [those] decisions" inside the White House and intelligence community, she added.
A FISA-like court process could go a long way to clearing up that ambiguity that exists within the administration's system of checks and balances in the drone strike program.
"I think we need to look at this whole process and try to find a way to make it transparent and verifiable," she said.
Senate intelligence panel member Ron Wyden (D-Org.) raised the issue of transparency on Thursday, pressing Brennan on whether CIA would publicly accept responsibility for mistakenly labeling an individual as a terror suspect and taking them out via armed drones.
Surprisingly, Brennan told Wyden and the Senate panel that under his leadership, CIA would be willing to publicly admit when an individual is mistakenly targeted and taken out by U.S. drones.
"As far as I am concerned ... the U.S. should [publicly] acknowledge it," he told the Senate panel.
Public admission of a mistaken drone strike, or the strike itself, would represent a break from the classified status of the entire U.S. armed drone strike program.
Last week, Feinstein, Leahy, Grassley and Durbin joined other House and Senate members in pressing the White House to release the classified DOJ legal memos on armed drone operations that formed the basis for the leaked white paper.
President Obama approved the release of the classified DOJ documents to Feinstein's committee last Wednesday, in anticipation of Brennan's confirmation hearing.
However, Grassley and his counterparts on the House Judiciary Committee demanded the White House release the documents to their panels as well.
"This committee has jurisdiction over the Constitution, and as a result, we should have access to these [DOJ] memos as well," the Iowa Republican told reporters last Tuesday, a day after NBC News reported the details of the white paper.
The drone strikes have played a key role in the Obama administration's increasingly aggressive counterterrorism campaign against al Qaeda. U.S. national security officials claim the strikes have decimated the terror group's top leaders in Afghanistan, Pakistan, Yemen and elsewhere.
But top civil rights groups, such as the American Civil Liberties Union, claim the counterterrorism tactic denies suspects — particularly U.S. citizens — their rights to due process in favor of national security objectives.