In its report on Thursday, The Washington Post said that the NSA is trying to develop a so-called "quantum computer" that could be used to break encryption codes used to cloak sensitive information.
Such a computer, which would be able to perform several calculations at once instead of in a single stream, could take years to develop, the newspaper said. In addition to being able to break through the cloaks meant to protect private data, such a computer would have implications for such fields as medicine, the newspaper reported.
The research is part of a $79.7 million research program called "Penetrating Hard Targets," the newspaper said. Other, non-governmental researchers are also trying to develop quantum computers, and it is not clear whether the NSA program lags the private efforts or is ahead of them.
Snowden, living in Russia with temporary asylum, last year leaked documents he collected while working for the NSA. The United States has charged him with espionage, and more charges could follow.
His disclosures have sparked a debate over how much leeway to give the US government in gathering information to protect Americans from terrorism, and have prompted numerous lawsuits.
Last week, a federal judge ruled that the NSA's collection of phone call records is lawful, while another judge earlier in December questioned the program's constitutionality. The issue is now more likely to move before the US Supreme Court.
On Thursday, the editorial board of the New York Times said that the US government should grant Snowden clemency or a plea bargain, given the public value of revelations over the National Security Agency's vast spying programs.
The New York Times and Guardian newspapers called Thursday for US leaker Edward Snowden to be granted clemency for his revelations on US government spying.
The two dailies in separate editorials hailed the fugitive computer specialist, who has sought refuge in Russia after leaking reams of information about the secretive US National Security Agency and its data gathering techniques.
"He may have committed a crime to do so, but he has done his country a great service," the Times wrote.
"It is time for the United States to offer Mr Snowden a plea bargain or some form of clemency."
Britain's Guardian newspaper meanwhile urged Washington "to allow Mr Snowden to return to the US with dignity," calling his revelations exposing the extent of Washington's electronic eavesdropping at home and abroad an act of "moral courage."
The Times called on the US government to offer Snowden a deal that "would allow him to return home (and) face at least substantially reduced punishment."
The National Security Council, President Barack Obama's in-house forum at the White House for national security and foreign affairs, on Thursday declined to comment, referring AFP to previous White House statements.
Obama has said he welcomes debate about the NSA's role as he weighs possible changes to its broad powers, but has refused to discuss the possibility of amnesty or a presidential pardon for Snowden.
In mid-December, the White House renewed its demand for the fugitive leaker to return home to face trial.
"Our position has not changed on that matter at all," White House spokesman Jay Carney said.