Two officials -- one from the Pentagon and the other a National Security Agency analyst -- were quoted by BuzzFeed as saying they wanted to kill Snowden personally.
"We are concerned with the situation around Edward. We see statements made by some U.S. officials containing potential and implicit threats to his life," Anatoly Kucherena told reporters in Moscow.
The Pentagon official, who was previously a U.S. Army Special Forces officer, was quoted in the BuzzFeed article Thursday as saying, "I would love to put a bullet in his head."
"I do not take pleasure in taking another human being's life, having to do it in uniform, but he is single-handedly the greatest traitor in American history," the official was quoted as saying.
The article, titled "America's Spies Want Edward Snowden Dead," said U.S. intelligence operators bristle at the thought of Snowden.
"In a world where I would not be restricted from killing an American, I personally would go and kill him myself," an NSA analyst told the website.
"A lot of people share this sentiment," the analyst said.
"Most everyone I talk to says he needs to be tried and hung -- forget the trial and just hang him," a U.S. defense contractor said.
An Army intelligence officer was quoted by BuzzFeed as describing how Snowden could be killed swiftly yet subtly.
"I think if we had the chance, we would end it very quickly," he said. "Just casually walking on the streets of Moscow, coming back from buying his groceries. Going back to his flat and he is casually poked by a passerby. He thinks nothing of it at the time, starts to feel a little woozy and thinks it's a parasite from the local water.
"He goes home very innocently and next thing you know he dies in the shower," the officer said.
"This is a real death threat, and we are concerned that it has prompted no reaction from anybody," Kucherena told reporters in remarks quoted by RIA Novosti.
"That is why we will file a request to the police," he said.
Kucherena told Russia-24 news channel Snowden was already accompanied by round-the-clock bodyguards, but given the threats, this "might not be enough" to ensure his safety.
Kucherena told reporters he would ask Russian law enforcement "to investigate all such statements" and Snowden U.S. legal adviser Ben Wizner would take steps in the United States to identify the officials who called for Snowden's assassination.
Snowden, 30, has taken refuge in Moscow to evade treason charges after disclosing U.S. state secrets on NSA intelligence gathering and revealing operational details of a global NSA-run surveillance apparatus targeting millions of people around the world.
The Pentagon had no immediate comment on Kucherena's news conference.
White House National Security Council spokeswoman said in a statement Snowden was an accused felon who needed to return to the United States to face federal criminal charges.
She said he would be "afforded all due process and protections."
U.S. Attorney General Eric Holder told Russia's justice minister in July Washington would not seek the death penalty for Snowden if he returned to the United States. He also said Snowden would not be tortured because torture in the United States was "unlawful."