Today on "This Week," Glenn Greenwald - the reporter who broke the story about the National Security Agency's surveillance programs - claimed that those NSA programs allowed even low-level analysts to search the private emails and phone calls of Americans.

"The NSA has trillions of telephone calls and emails in their databases that they've collected over the last several years," Greenwald told ABC News' George Stephanopoulos. "And what these programs are, are very simple screens, like the ones that supermarket clerks or shipping and receiving clerks use, where all an analyst has to do is enter an email address or an IP address, and it does two things. It searches that database and lets them listen to the calls or read the emails of everything that the NSA has stored, or look at the browsing histories or Google search terms that you've entered, and it also alerts them to any further activity that people connected to that email address or that IP address do in the future."

Greenwald explained that while there are "legal constraints" on surveillance that require approval by the FISA court, these programs still allow analysts to search through data with little court approval or supervision.

"There are legal constraints for how you can spy on Americans," Greenwald said. "You can't target them without going to the FISA court. But these systems allow analysts to listen to whatever emails they want, whatever telephone calls, browsing histories, Microsoft Word documents."

"And it's all done with no need to go to a court, with no need to even get supervisor approval on the part of the analyst," he added.

But the top Republican on the Senate Intelligence Committee told Stephanopoulos he would be shocked if such programs existed.

"It wouldn't just surprise me, it would shock me," Sen. Saxby Chambliss, R-Georgia, said on "This Week" Sunday.

Chambliss said he recently spent time with NSA officials and was assured that the programs Greenwald describes have been exaggerated.

"I was back out at NSA just last week, spent a couple hours out there with high and low level NSA officials," Chambliss said. "And what I have been assured of is that there is no capability at NSA for anyone without a court order to listen to any telephone conversation or to monitor any e-mail."

Chambliss said that any monitoring of emails is purely "accidental."

"In fact, we don't monitor emails. That's what kind of assures me is that what the reporting is is not correct. Because no emails are monitored now," Chambliss said. "They used to be, but that stopped two or three years ago. So I feel confident that there may have been some abuse, but if it was it was pure accidental."

But Greenwald said the existence of these analyst search programs are in line with the claims of Edward Snowden, who first leaked details of the NSA's surveillance programs last month.

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"It's an incredibly powerful and invasive tool, exactly of the type that Mr. Snowden described," Greenwald said.

NSA Director Gen. Keith Alexander and House Intelligence leaders have previously downplayed Snowden's access to NSA data. Greenwald said the revelation of this search capability deserves a response from NSA officials when they testify before Congress again this week.

"NSA officials are going to be testifying before the Senate on Wednesday, and I defy them to deny that these programs work exactly as I just said," Greenwald said.

Greenwald, who will join via video-link a separate bipartisan congressional group hearing from critics of the NSA's surveillance programs on Wednesday, called on lawmakers to push for more information about the NSA's practices.

"The real issue here is that what the NSA does is done in complete secrecy. Nobody really monitors who they are eavesdropping on," Greenwald said. "So the question of abuse is one that the Congress ought to be investigating much more aggressively."

Snowden, the former NSA contractor who leaked information about two sweeping intelligence programs, has previously warned that they are open to abuse by those with access. In a video interview with The Guardian , he said, "Any analyst at any time can target anyone… I, sitting at my desk, had the authority to wiretap anyone, from you or your accountant to a federal judge to even the president if I had a personal email."

Snowden has been holed up in a Moscow airport for weeks. He is currently attempting to secure temporary asylum in Russia on the grounds that he would be tortured or face the death penalty if he returned to the United States.

Attorney General Eric Holder responded to Snowden's appeal last week, writing in a letter to the Russian government, "These claims are entirely without merit."

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Today, Greenwald told Stephanopoulos that Snowden's petition is still pending, but the former NSA contractor prefers that the focus be elsewhere.

"I think he's content with having nothing happen so the focus isn't on him, but is on the substance of the revelations that he came forward to shine light on," Greenwald said.

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Grey Korhonen contributed to this report.