(CNN) -- American intelligence leaker Edward Snowden has more damaging information that could be a "nightmare" for the U.S. government, a journalist who first published his documents said.
Glenn Greenwald of the Guardian told an Argentine newspaper, La Nacion, that releasing more information to hurt the United States is not Snowden's goal.
However, he said, Snowden has a "large number" of documents about software people use "without consciously agreeing to surrender their rights to privacy."
Snowden has given copies of the papers to several people, Greenwald told the paper, according to an English translation.
"The U.S. government should be on their knees every day praying that nothing happens to Snowden, because if something happens, all information will be revealed and that would be their worst nightmare," he said.
Others have suggested this before.
Kristinn Hrafnsson, a WikiLeaks spokesman, said last month that other secrets may be revealed.
"There is more to come," he said.
Snowden is a former computer technician for U.S. defense contractor Booz Allen Hamilton.
In June, he gave Greenwald and colleague Ewen MacAskill a 12-minute video interview on why he provided the Guardian the classified documents about U.S. surveillance programs.
Following his revelation, he fled to Hong Kong, then headed to Russia, where he is in political limbo in the transit area of a Moscow airport. He has requested asylum from Russia while he awaits safe passage to Latin America, according to WikiLeaks.
No application from Snowden has yet been received, the head of the Russian Federal Migration Service, Konstantin Romodanovsky, told the nation's news agency, Interfax.
The presidents of Venezuela and Bolivia have said their countries would give him asylum, and Nicaragua's president said he would offer it "if circumstances permit."
Snowden faces espionage charges in the United States.
He met with human rights activists and lawyers Friday at the airport. It was his first public appearance since he left Hong Kong on June 23.
"I announce today my formal acceptance of all offers of support or asylum I have been extended and all others that may be offered in the future," he said in a statement.
"As we have seen, however, some governments in Western European and North American states have demonstrated a willingness to act outside the law, and this behavior persists today. This unlawful threat makes it impossible for me to travel to Latin America and enjoy the asylum granted there in accordance with our shared rights."
In his remarks, Snowden also sought to defend his actions in leaking documents to the media that exposed U.S. mass surveillance programs.
"I did what I believed right and began a campaign to correct this wrongdoing. I did not seek to enrich myself. I did not seek to sell US secrets. I did not partner with any foreign government to guarantee my safety. Instead, I took what I knew to the public, so what affects all of us can be discussed by all of us in the light of day, and I asked the world for justice," he said.
"That moral decision to tell the public about spying that affects all of us has been costly, but it was the right thing to do and I have no regrets."
The United States has reached out to the Russians regarding Snowden's meeting with human rights groups, two senior State Department officials told CNN.
CNN's Marilia Brocchetto contributed to this report.