(CNN) - Republican Rep. Justin Amash of Michigan said Sunday he's hopeful the House will have another chance to vote on a measure that would curb the National Security Agency.
The Washington Post reported Friday that an internal NSA audit showed that the agency broke privacy rules "thousands of times each year," by making illegal interceptions of phone calls and e-mails, using methods later deemed illegal, and not fully reporting the extent of the agency's errors.
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The report renewed calls from lawmakers to dig further into the agency's operations.
"The system is not working," Amash said on CNN's "State of the Union."
"Americans were told by the chairman of the House Intelligence Committee that there were zero privacy violations, and we know that's not true," he continued. "Americans were assured by the president and others that the (Foreign Intelligence Surveillance Act) court had significant oversight, and we've heard from the chief judge of the FISA court who says that's not true."
The House last month narrowly defeated a measure drafted by Amash that would have restricted the NSA's federal surveillance program that monitors domestic phone records and was exposed by former NSA contractor Edward Snowden.
Following the Post's latest report, Sen. Patrick Leahy, D-Vermont, said Friday the Senate Judiciary Committee he chairs will hold a hearing on the new revelation.
In a call with reporters Friday, John DeLong – the NSA's director of compliance - acknowledged "mistakes occur," even as he insisted only a "tiny" number of such problems were intentional.
"No one at NSA thinks a mistake is OK," DeLong said several times in the call, which a spokesman said was conducted to "address inaccuracies."
Rep. Chris Van Hollen, D-Maryland, who voted against the Amash amendment that would have ended some of the NSA's capabilities, said Sunday he doesn't have any second thoughts about his vote last month but added he has "serious concerns" about the NSA.
"The amendment I don't think did the trick, frankly. I think there are much more important things we need to be doing," he said on "State of the Union."
Van Hollen called for broader reforms to the Patriot Act and said a citizen's advocate was needed to take the adversarial position before the FISA court, rather than the NSA going before the court unilaterally.
"We should have somebody at the court whose jobs it is, whose responsibility is to make sure they're putting forth the counterargument," he told CNN's chief political correspondent Candy Crowley. "In the court of law, you have two parties. The court itself should make a decision between two arguments. Right now, the (FISA) court is only hearing one argument."
Republican Sen. Rand Paul of Kentucky, who has been a critic of the NSA programs since word of them was leaked in June, said he agrees there should be more oversight, but argued further that some of the NSA's operations are "fundamentally unconstitutional."
"The constitution doesn't allow for a single warrant to get a billion phone records. They have a warrant that says they want all of Verizon's phone calls," he said on "Fox News Sunday." "Also, I don't think it's good police work. I think we get overwhelmed with data."
Rep. Peter King, R-New York, a supporter of the programs, said he fully disagrees with Paul and other critics of the NSA. King, also speaking on Fox, said Paul's remarks were "a grab bag of misinformation and distortion."
"Take Rand Paul's own numbers. He said there are billions of phone calls being collected," King continued. "It's not really true, but assume he's right for once. Billions of phone calls being collected. You juxtapose that with 2,800 violations, which were self-reported by the NSA."
King added that 1,900 of those violations were on foreign phones and "no American's rights were violated because of that." The longtime congressman argued it's scandalous to say the government agency used the information "to hurt people."
"Whatever mistakes were made were inadvertent. 99.99% batting average, that's better than most media people do, most politicians do," he said, adding he has "tremendous respect" for the NSA's chief, Gen. Keith Alexander. "This whole tone of 'snooping' and 'spying' that we use, I think is horrible."
- CNN's Dan Merica and Ed Payne contributed to this report.