White House adviser Dan Pfeiffer and the heads of America's Senate and House intelligence committees spoke just days after a German lawmaker published a letter from the fugitive and said Snowden was ready to testify to Congress to shed light on "possibly serious offenses."
"Mr Snowden violated US law," Pfeiffer told ABC television's This Week program. "He should return to the US and face justice."
But Senator Dianne Feinstein said the former National Security Agency (NSA) contractor had missed his chance.
"He had an opportunity, if what he was a whistleblower to pick up the phone and call the House Intelligence Committee, the Senate Intelligence Committee and say, 'Look, I have some information you ought to see,'" she told CBS television's Face the Nation.
"We would have seen him and we would have looked at that information. That didn't happen, and now he's done this enormous disservice to our country. "And I think the answer is no clemency," said the California Democrat, adding that Snowden should be prosecuted.
Snowden was granted asylum in Russia in August to the fury of the United States, where he is wanted on espionage charges.
Congressman Mike Rogers, a Republican, said he didn't see "any reason" to clear Snowden of any possible charges.
"If he wants to come back and own up to the responsibility of the fact that he took and stole information, he violated his oath, he disclosed classified information... I'd be happy to have that discussion with him," Rogers told the CBS program.
"But he does need to own up with what he's done and if he wants to talk through why he did it and those things, that would be the appropriate time and the appropriate way to do it."
German Green Party lawmaker Hans-Christian Stroebele met with Snowden late Thursday at an undisclosed location in Moscow to discuss his revelations that Washington monitored German Chancellor Angela Merkel's cellphone, a matter that caused an uproar in Europe.
Feinstein appeared to question the purpose of such monitoring.
"I think where allies are close, tapping private phones of theirs, particularly of the leader, the leader is what I'm talking about, has much more political liability than probably intelligence viability," she said.
"And I think we ought to look at it carefully; I believe the president is doing that and there are some exceptions."
In a separate Face the Nation interview, former NSA and Central Intelligence Agency chief Michael Hayden suggested Germany had bigger woes on the spying front.
"I know the Chancellor's embarrassed and we're a friend and this revelation has put her in a very difficult political spot," the retired general said.
"Frankly, in the world of espionage, the fact that the United States may have been intercepting her text messages is the least of their espionage worries in Berlin right now."
In a "manifesto for the truth" published in German news magazine Der Spiegel, Snowden said mass secret surveillance poses a threat to freedom of expression and open society and that systematic snooping was a global problem that needed global solutions.
He said in the letter handed to Stroebele that he was prepared to provide details of US spying to Germany and was "heartened" by the global response to his leaks despite unrelenting American pressure.
The letter was addressed to the German government, the Bundestag lower house of parliament and the federal public prosecutor, Stroebele's office said.
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@Pasanni: Off course,Pakistan has forgiven Dr. Shakil Afridi for helping to bring to justice the most notorious terrorist in the world.
And what about freedom of speech?? where is Asma Jihangir???