Deputy director of the NSA John Inglis (left) is among the officials to be questioned by the SenateThe declassification was made in the "interest of increased transparency", intelligence officials said.
But significant parts of the three released documents were redacted.
Meanwhile the father of Edward Snowden, who leaked information about the surveillance, says the FBI has asked him to go to Moscow to see his son.
Also on Wednesday, the UK's Guardian newspaper published slides leaked by Edward Snowden that detail a secret US surveillance system known as XKeyscore.
It reportedly enables American intelligence to monitor "nearly everything a typical user does on the internet".
The programme includes real-time data and suggests analysts could narrow searches through use of so-called metadata also stored by the National Security Agency (NSA), America's electronic intelligence organisation, the newspaper reports.
Blacked out
The official US documents released on Wednesday include a court order describing how the data from the phone-snooping programme would be stored and accessed.
Two reports to US lawmakers on the telephone and email records were also declassified.
But lines in the files, including details on "selection terms" used to search the massive data stores, were blacked out.
Deputy Attorney General James Cole told a Senate judiciary committee hearing on Wednesday that the court order spells out how the government can use call data obtained from telecom giants such as Verizon.
For the first time, the government acknowledged publicly that by using what it calls "hop analysis" it can scour the phone calls of millions of Americans in the hunt for just one suspect.
NSA analysts could use the records of everyone a suspect calls, as well as everyone who contacts the contacts of contacts of the initial suspect.
If the average person calls 40 unique people, such three-hop analysis could allow the government to mine the records of 2.5 million Americans when investigating one suspected terrorist.
"What's being described as a very narrow programme is really a very broad programme," Democratic Senator Richard Durbin said.
But the head of the NSA, General Keith Alexander, remained unapologetic about the agency's methods at a hacker conference in Las Vegas on Wednesday, insisting the programme had prevented attacks on the US.
'Find a safe haven'
Wednesday's was the first congressional session on the issue since the House narrowly rejected a proposal effectively to shut down the NSA's secret collection of hundreds of millions of Americans' phone records.
How the US collects phone records
The National Security Agency (NSA) began collecting Americans' phone records in 2001, as part of far-reaching surveillance programmes launched by then-President George W Bush in the aftermath of the 9/11 attacks.
But the scope of the practice, continued under President Barack Obama, only became apparent in June when ex-CIA contractor Edward Snowden leaked classified US surveillance files. It emerged that a US secret court had ordered phone company Verizon to hand over to the NSA the phone records of tens of millions of American customers.
This information, known as metadata, includes the numbers of the originating and receiving phone, the call's duration, time, date and location (for mobiles, determined by which mobile signal towers relayed the call or text). The contents of the conversation itself, however, are not covered, US intelligence officials say. The surveillance applies to calls placed within the US, and calls between the US and abroad.
During the early parts of the hearing, NSA deputy director John Inglis said "no" when asked if anyone had been fired over the leak.
"No-one has offered to resign," Mr Inglis said. "Everyone is working hard to understand what happened."
Democratic Senator Patrick Leahy, the chairman of the committee, also questioned the deputy director on the number of attacks the agency said had been disrupted by the programmes.
Gen Alexander has said phone and internet surveillance disrupted 54 schemes by militants.
Sen Leahy said a list of the relevant plots provided to Congress does not reflect dozens, as he said, "let alone 54 as some have suggested".
Mr Inglis said the phone surveillance helped disrupt or discover attacks 12 times, and the larger number were foiled thanks to both the phone-records snooping and a second programme collecting global internet users' data.
Meanwhile, Edward Snowden's father, Lon, told Russian state TV he does not believe his son would get a fair trial in America and that the fugitive should stay in Russia.
In the interview, the elder Snowden thanked the Russian authorities for keeping his son safe and advised the 29-year-old "to find a safe haven".
Edward Snowden, a former NSA contractor, has been stuck in a transit area at a Moscow airport for more than a month after the US revoked his travel documents.
bbc.com