Senate intelligence panel Chairwoman Dianne Feinstein said she wants a full review of National Security Agency spy operations in light of the global furor over accusations the agency eavesdropped on key European leaders.

The California Democrat told CBS's "Face the Nation" Sunday she will work with her counterparts on the House intelligence committee to "put together a review of the intelligence framework, of how all this gets together, what the criteria for inclusion are."

"The White House is doing [a review] and we're going to begin [with one in Congress] if we can get the appropriate staff to conduct it," she said.

The NSA has been hammered in recent weeks over media reports, based on information leaked by former NSA contractor Edward Snowden, that the agency has tracked the phone calls of millions of ordinary citizens in Western Europe for more than a decade. Among those spied on, the reports say, were several world leaders, including German Chancellor Angela Merkel.

Feinstein said that while she doesn't know if Merkel's phone was tapped, spying on foreign allies "has much more political liability than probably intelligence viability."

"We ought to look at it carefully, [and] I believe the president is doing that," she said.

Feinstein stopped short of saying the agency went too far in its spying methods and policies, saying she believes the NSA "is filled with good, patriotic people who want to do the right thing."

"They follow the orders they're given," she said.

Rep. Mike Rogers, R-Mich., chairman of the House Permanent Select Intelligence Committee, said a blanket condemnation of the agency, which oversees U.S. intelligence gathering operations worldwide, would be wrong.

"We focused a lot on the NSA ... but not a lot about what the threat is," Rogers said on "Face the Nation."

"What we've asked them to do is go out and collect information that protects America. So every politician in Washington, both Republican and Democrat, are seized up by this hyperpartisanship and can't wait to put out a press release how terrible our intelligence services are."

Rogers also warned against reining in U.S. spying agencies, saying doing so would compromise national security.

"We did the same darn thing leading up to the Osama bin Laden effort, where [U.S. intelligence agencies] didn't want to talk to each other, we didn't coordinate intelligence activities, we didn't want to get certain things, and it led to 9/11 that took the lives of 3,000 Americans," he said.

When asked if he believed the White House when it said President Obama didn't know Merkel's phone was tapped, Rogers said "there's going to be some best actor awards coming out of the White House this year and best supporting actor awards coming out of the European Union."