The National Security Agency revealed to an angry congressional panel on Wednesday that its analysis of phone records and online behavior goes exponentially beyond what it had previously disclosed.

John C Inglis, the deputy director of the surveillance agency, told a member of the House judiciary committee that NSA analysts can perform "a second or third hop query" through its collections of telephone data and internet records in order to find connections to terrorist organizations.

"Hops" refers to a technical term indicating connections between people. A three-hop query means that the NSA can look at data not only from a suspected terrorist, but from everyone that suspect communicated with, and then from everyone those people communicated with, and then from everyone all of those people communicated with.

Inglis did not elaborate, nor did the members of the House panel – many of whom expressed concern and even anger at the NSA – explore the legal and privacy implications of the breadth of "three-hop" analysis.

But Inglis and other intelligence and law enforcement officials testifying before the committee said that the NSA's ability to query the data follows rules set by the secret Fisa court, although about two dozen NSA officials determine for themselves when those criteria are satisified.

A document published last month by the Guardian detailing the history of the NSA's post-9/11 bulk surveillance on telephone and internet data refer to one- or two-hop analysis performed by NSA. The document, provided by ex-NSA contractor Edward Snowden, does not explicitly mention three-hop analysis, nor does it clearly suggest that such analysis occurs.

Wednesday's hearing was the second major public congressional hearing about the NSA's surveillance activities since the Guardian and the Washington Post disclosed some of them in early June. Unlike the previous hearing on June 18 before the House intelligence committee, members of the House judiciary committee aggressively questioned senior officials from the NSA, FBI, Justice Department and Office of the Director of National Intelligence.

One senior member of the panel, congressman James Sensenbrenner, the author of the 2001 Patriot Act, warned the officials that unless they rein in the scope of their surveillance on Americans' phone records, "There are not the votes in the House of Representatives" to renew the provision after its 2015 expiration.

"You're going to lose it entirely," Sensenbrenner said.

Inglis and deputy attorney general James Cole repeatedly argued that the NSA's surveillance was limited because it only searches through its databases of phone records when it has a "reasonable, articulable suspicion" of a connection to terrorism.

But several members of the committee, of both parties, said they were concerned not merely about the analysis of the phone records but about NSA's collection of millions of Americans' phone data in the first place, without an individual suspicion of connections to terrorism.

"The statute says 'collection'," congressman Jerrold Nadler told Cole. "You're trying to confuse us by talking use."

Congressman Ted Poe, a judge, said: "I hope as we move forward as a Congress we rein in the idea that it's OK to bruise the spirit of the constitution in the name of national security."

Inglis, Cole and Robert Litt, the senior legal counsel for the Office of the Director of National Intelligence, also argued that the surveillance activities were restricted by the oversight of Congress and the Fisa court. Legislators challenged both contentions.

Congressman Spencer Bachus said he "was not aware at all" of the extent of the surveillance, since the NSA programs were primarily briefed to the intelligence committees of the House and Senate.

Congresswoman Zoe Lofgren revealed that an annual report provided to Congress by the government about the phone-records collection, something cited by intelligence officials as an example of their disclosures to Congress, is "less than a single page and not more than eight sentences".

Congressman Hakeem Jeffries, challenged Litt's contention that the Fisa court was "not a rubber stamp" by way of a baseball analogy. Jeffries noted that some of the greatest hitters in baseball history – the Cardinals' Stan Musial, the Red Sox's Ted Williams, the Tigers' Ty Cobb and the Yankees' Babe Ruth – did not hit more than four balls safely per 10 times at bat, for career batting averages ranging from Musial's .331 to Cobb's .366.

He then noted that the Fisa court approves over 99% of government requests for surveillance – which would give the government a lifetime batting average of .999 – saying: "But you've taken the position that the Fisa court is an independent check."

Litt, continuing the analogy, said that when the government submits a surveillance request or "throws a pitch", the Fisa court "says 'throw a little bit higher, a little more inside'" rather than ruling it out of the strike zone.