A remark by Director of National Intelligence James R. Clapper Jr., has perhaps drawn the most attention. Asked during a congressional hearing in March whether the NSA collected data on millions of Americans, Clapper replied, “No, sir.” (Susan Walsh/AP)

Amid the cascading disclosures about National Security Agency surveillance programs, the top lawyer in the U.S. intelligence community opened his remarks at a rare public appearance last week with a lament about how much of the information being spilled was wrong.

“A lie can get halfway around the world before the truth gets its boots on,” said Robert Litt, citing a line often attributed to Mark Twain. “Unfortunately, there’s been a lot of misinformation that’s come out about these programs.”

The remark by Litt, general counsel for the Office of the Director of National Intelligence, was aimed at news organizations. But details that have emerged from the exposure of hundreds of pages of previously classified NSA documents indicate that public assertions about these programs by senior U.S. officials have also often been misleading, erroneous or simply false.

The same day Litt spoke, the NSA quietly removed from its Web site a fact sheet about its collection activities because it contained inaccuracies discovered by lawmakers.

A week earlier, President Obama, in a television interview, asserted that oversight of the surveillance programs was “transparent” because of the involvement of a special court, even though that court’s sessions and decisions are sealed from the public. “It is transparent,” Obama said of the oversight process. “That’s why we set up the FISA court.”

See the inner workings of the NSA’s PRISM program

A remark by Litt’s boss, Director of National Intelligence James R. Clapper Jr., has perhaps drawn the most attention. Asked during a congressional hearing in March whether the NSA collected data on millions of Americans, Clapper replied, “No, sir.”

U.S. officials have cited a variety of factors to explain the discrepancies, including the challenge of speaking publicly and definitively about programs that remain classified and involve procedures and technical systems that are highly complex.

Jane Harman, a former ranking Democrat on the House Intelligence Committee, said that speaking about secret programs can be a “minefield” for public officials.

“Are people deliberately misleading other people? I suppose it can happen,” Harman said in an interview. Facts can be obscured through “selective declassification that means you put out some pieces but not others,” she said. “But I assume most people are acting in good faith.”

Acknowledging the “heated controversy” over his remark, Clapper sent a letter to the Senate Intelligence Committee on June 21 saying that he had misunderstood the question he had been asked.

“I have thought long and hard to re-create what went through my mind at the time,” Clapper said in the previously undisclosed letter. “My response was clearly erroneous — for which I apologize.”

Beyond inadvertent missteps, however, an examination of public statements over a period of years suggests that officials have often relied on legalistic parsing and carefully hedged characterizations in discussing the NSA’s collection of communications.

Obama’s assurances have hinged, for example, on a term — targeting — that has a specific meaning for U.S. spy agencies that would elude most ordinary citizens.

“What I can say unequivocally is that if you are a U.S. person, the NSA cannot listen to your telephone calls and the NSA cannot target your e-mails,” Obama said in his June 17 interview on PBS’s “Charlie Rose Show.”

But even if it is not allowed to target U.S. citizens, the NSA has significant latitude to collect and keep the contents of e-mails and other communications of U.S. citizens that are swept up as part of the agency’s court-approved monitoring of a target overseas.

The law allows the NSA to examine such messages and share them with other agencies if it determines that the information contained is evidence of a crime, conveys a serious threat or is necessary to understand foreign intelligence.

The threshold for scrutinizing other data not regarded as content but still potentially revealing is lower than it is for the contents of communications. A 2009 report by the NSA inspector general and obtained by The Washington Post indicates that the agency for years examined metadata on e-mails flowing into and out of the United States, including “the sender and recipient e-mail addresses.”

President George W. Bush at times engaged in similarly careful phrasing to defend surveillance programs in the years after the Sept. 11, 2001, attacks. In 2004, while calling for renewal of the Patriot Act, Bush sought to assuage critics by saying “the government can’t move on wiretaps or roving wiretaps without getting a court order.”

At the time, it had not yet been publicly disclosed that Bush had secretly authorized NSA surveillance of communications between U.S. residents and contacts overseas while bypassing the Foreign Intelligence Surveillance Court.

When the wiretapping operation was exposed in the news media two years later, Bush defended it as a program “that listens to a few numbers, called from outside of the United States, and of known al-Qaeda or affiliate people.” Subsequent revelations have made clear that the scope was far greater than his words would suggest.

News accounts of the NSA programs have also contained inaccuracies, in some cases because of the source materials. Classified NSA slides that were published by The Post indicated that the NSA was able to tap directly into the servers of Google, Microsoft, Apple and other technology companies. The companies denied that they allowed direct access to their equipment, although they did not dispute that they cooperated with the NSA.

Current and former U.S. officials have defended the programs, and some have called for greater transparency as a way of allaying concerns.

“I’m convinced, the more the American people know exactly what it is we are doing in this balance between privacy and security — the more they know, the more comfortable they will feel,” Michael V. Hayden, former director of the NSA and CIA, told “Face the Nation” on Sunday. “Frankly, I think we ought to be doing a bit more to explain what it is we’re doing, why, and the very tight safeguards under which we’re operating.”

For now, the crumbling secrecy surrounding the programs has underscored the extent to which obscuring their dimensions had served government interests beyond the importance of the intelligence they produced.

Secret court rulings that allowed the NSA to gather phone records enabled the spy service to assemble a massive database on Americans’ phone records without public debate or the risk of political blowback.

The binding secrecy built into the PRISM program of tracking international e-mail allowed the NSA to compel powerful technology companies to comply with requests for information about their users while keeping them essentially powerless to protest.

The careful depiction of NSA programs also served diplomatic ends. Until recently, the United States had positioned itself as such an innocent victim of cyber intrusions by Russia and China that the State Department issued a secret demarche, or official diplomatic communication, in January scolding Beijing. That posture became more problematic after leaks by the former NSA contractor and acknowledged source of the NSA leaks, Edward Snowden, who fled to Hong Kong and is thought to be stuck at Sheremetyevo International Airport in Moscow.

Clapper’s testimony before the Senate Intelligence Committee in March has drawn comparisons to other cases in which U.S. intelligence officials faced, under oath, questions that to answer truthfully would require exposing a classified program.

In 1973, then-CIA Director Richard Helms denied agency involvement in CIA operations in Chile, a falsehood that led to him pleading no contest four years later to misdemeanor charges of misleading Congress.

There is no indication that lawmakers have contemplated pursuing such a course against Clapper, in part because he subsequently corrected his claim, although there is disagreement over how quickly he did so.

Sen. Ron Wyden (D-Ore.), who had asked Clapper the question about information collection on Americans, said in a recent statement that the director had failed to clarify the remark promptly despite being asked to do so. Clapper disputed that in his note to the committee, saying his “staff acknowledged the error to Senator Wyden’s staff soon after the hearing.”

In early June, after the NSA leaks had brought renewed attention to Clapper’s “No, sir,” Clapper cited the difficulty of answering a question about a classified program and said in an interview on NBC News that he had responded in the “least most untruthful manner.”

He made a new attempt to explain the exchange in his June 21 correspondence, which included a hand-written note to Wyden saying that an attached letter was addressed to the committee chairman but that he “wanted [Wyden] to see this first.”

Clapper said he thought Wyden was referring to NSA surveillance of e-mail traffic involving overseas targets, not the separate program in which the agency is authorized to collect records of Americans’ phone calls that include the numbers and duration of calls but not individuals’ names or the contents of their calls.

Referring to his appearances before Congress over several decades, Clapper concluded by saying that “mistakes will happen, and when I make one, I correct it.”

Julie Tate contributed to this report.