Keith Alexander testifies to Congress that programs revealed by Edward Snowden have stopped 'more than 50' attacks

Some of the most senior intelligence and law enforcement officials in the United States strongly defended the National Security Agency's broad surveillance efforts on Tuesday, saying they had disrupted more than 50 terrorist plots around the world.

General Keith Alexander, the director of the NSA, told a rare public hearing of the House intelligence committee in Washington that the programs were "critical" to the ability of the intelligence community to protect the US.

Offering the most extensive defence yet on the efficacy of secret surveillance programs reported by the Guardian and the Washington Post, Alexander said they were "limited, focused and subject to rigorous oversight".

During the hearing, members of Congress criticised the source of the leaks, Edward Snowden, who remains free in Hong Kong. On Tuesday, Iceland said it had received an informal approach from an intermediary claiming that Snowden, a 29-year-old former NSA contractor, wanted to seek asylum there. Asked at the congressional hearing about what was next for Snowden, Alexander said: "justice".

Flanked by senior officials from the FBI, Justice Department and the Office of the Director of National Intelligence, Alexander said that two surveillance programs revealed by the Guardian and the Washington Post had "helped prevent more than 50" terrorist attacks in over 20 countries.

Most of those prevention efforts, Alexander said, came from the NSA's monitoring of foreigners' internet communications under a program known as Prism. He conceded that only 10 related to domestic terror plots.

The Obama administration officials gave more details about four cases in which information taken from the NSA's databases of foreign internet communications and millions of Americans' phone records had contributed to stopping attacks. Two of them have been previously disclosed, especially that of the 2009 arrest of would-be New York subway bomber Najibullah Zazi. That case has been sharply challenged thanks to court records as more attributable to traditional police surveillance.

Referring to the statutory authority for Prism, known as Section 702 of the 2008 Fisa Amendments Act, FBI deputy director Sean Joyce said: "Without the 702 tool, we would not have identified Najibullah Zazi."

Joyce identified two previously unknown cases that he said the surveillance efforts helped unravel. In one, a Kansas City, Missouri, man named Khalid Ouazzani was found communicating with a "known extremist" in Yemen, information that helped detect what Joyce called "nascent plotting" to bomb the New York Stock Exchange. The other, described more vaguely, allowed the US government, using the NSA's phone-records database of Americans, to revisit a case closed shortly after 9/11 for lack of evidence.

Ouazzani, however, was never convicted of plotting to bomb the stock exchange. Andrew Ames, a Justice Department spokesman, later clarified that he was convicted of "sending funds" to al-Qaida. The other case, Joyce said, involved an American who provided "financial support" to extremists in Somalia.

Two members of the Senate intelligence committee, Ron Wyden and Mark Udall, said last week that they had not seen any evidence to show that the "NSA's dragnet collection of Americans' phone records has produced any uniquely valuable intelligence".

The intelligence and law enforcement officials as subject to "checks and balances". But they clarified, in the most detail provided publicly thus far, that most of those checks are internal.

James Cole, the deputy attorney general, said that the NSA needs "reasonable, articulable suspicion" of involvement in terrorism before searching the millions of Americans' phone records that it collects. But, Cole said: "We do not have to get separate court approval for each query."

Instead, the NSA sends an "aggregate number" of times it has searched the database every 30 days to the secret Fisa court that oversees surveillance, while also sending a separate report each time NSA analysts inappropriately search the database. Alexander's deputy, Chris Ingliss, said NSA analysts searched the database 300 times in 2012 in total.

Representative Adam Schiff, Democrat of California, said that "it may be valuable to have court review prospectively".

Alexander pledged to send the House and Senate intelligence committees greater detail on the surveillance programmes' role in preventing the 50-plus plots in secret on Wednesday. But he insisted the NSA took great care internally to balance civil liberties and national security.

"I would much rather today be here to debate this point than try to explain why we failed to prevent another 9/11," he said.