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Greenwald said he himself has beefed up his own security, particularly since a laptop went missing from his Rio home.
"I don't really feel comfortable discussing the specific measures, but one would be really irrational and foolish to have thousands of top-secret documents from the most secretive agency of the world's most powerful government and not be thoughtful about added security," said the 46-year-old former constitutional and civil rights lawyer who has written three books contending the government has violated personal rights in the name of protecting national security.
Greenwald has also co-authored a series of articles in Rio de Janeiro's O Globo newspaper focusing on NSA actions in Latin America. He said he expected to continue publishing further stories based on other Snowden documents over the next four months.
Upcoming stories would likely include details on "other domestic spying programs that have yet to be revealed," but which are similar in scope to those he has been reporting on. He did not provide further details on the nature of those programs.
It was not immediately clear whether Russia would take Snowden up on his latest request for asylum, which could further test U.S.-Russia relations.
Following Friday's meeting between Snowden and human rights activists, U.S. officials criticized Russia for allowing a "propaganda platform" for the NSA leader.
White House spokesman Jay Carney said Russia should instead send Snowden back to the U.S. to face the felony charges that are pending against him.
Carney said Snowden is not a human rights activist or a dissident. "He is accused of leaking classified information, has been charged with three felony counts and should be returned to the United States," the spokesman said.