The US director of national intelligence, James Clapper, has attempted to head off criticism that he lied to Congress over the extent of government surveillance on American citizens, with a letter to senators in which he apologised for giving "erroneous" information.

Two weeks after telling NBC news that he gave the "least untruthful answer possible" at a hearing in March, Clapper wrote to the Senate intelligence committee to correct his response to a question about whether the National Security Agency "collected data on millions of Americans".

During the orginal hearing on 12 March, Clapper answered "no, sir," to a question by Senator Ron Wyden. It emerged later that Wyden had given him 24 hours notice of the question, and after the session ended, offered him an opportunity to correct it, which was declined.

After disclosures by former NSA contractor Edward Snowden detailing the collection of millions of American phone records, pressure grew on Clapper to clarify his remarks. In an interview with Andrea Mitchell of MSNBC, portions of which were first broadcast on 9 June, after Snowden's leaks first emerged in the Guardian, Clapper explained the apparent inconsistency as a ploy to avoid revealing classified information.

On 18 June, Republican senator Rand Paul, of Kentucky, accused Clapper directly of lying, pointed out that lying on oath to Congress was a crime, and questioned whether he could continue in his position.

According to the latest revelation in the Washington Post on Monday, Clapper wrote to the Senate intelligence committee on 21 June, when he admitted directly that his answer was wrong. "My response was clearly erroneous – for which I apologize," Clapper said in the letter.

The Office of the Director of National Intelligence did not respond to requests by the Guardian to confirm the contents of the letter.

In his MSNBC interview, Clapper said he believed Wyden's question was unfair, akin to asking him when he was going to stop beating his wife. "So I responded in what I thought was the most truthful, or least untruthful, manner by saying no," Clapper said.

In the later letter to the intelligence committee, Clapper acknowleded the "heated controversy" over his remark, and said he had misunderstood the original question. "I have thought long and hard to re-create what went through my mind at the time," Clapper said in the letter, according to the Washington Post.

The question was posed by Oregon Democrat Ron Wyden, who grew frustrated that he could not get a "direct answer" from Clapper about a question Wyden said he had been posing to the intelligence agencies in a series of letters for a year: when do US spies need a warrant to surveil Americans' communications?

"What I wanted to see is if you could give me a yes or no answer to the question: does the NSA collect any type of data at all on millions or hundreds of millions of Americans," Wyden asked Clapper.

He responded: "No, sir, not wittingly. There are cases where they could inadvertently, perhaps, collect, but not wittingly."

Last week Wyden, Democrat of Oregon, led a bi-partisan group of 26 senators who wrote to Clapper to complain that the administration is relying on a "secret body of law" to collect massive amounts of data on US citizens.

The senators, including four Republicans, also accused intelligence chiefs of making a number of misleading statements which prevented proper public debate on the subject.

"We are concerned that by depending on secret interpretations of the Patriot Act that differed from an intuitive reading of the statute, this program essentially relied for years on a secret body of law," they said.

"This and misleading statements by intelligence officials have prevented our constituents from evaluating the decisions that their government was making, and will unfortunately undermine trust in government more broadly." © Guardian News and Media 2013