Snowden was a Hawaii-based computer network administrator for Booz Allen Hamilton, an NSA contractor. Alexander said Snowden "betrayed the trust and confidence we had in him" and is "not acting, in my opinion, with noble intent."
Greenwald said Snowden has been extremely judicious about what he has revealed.
"I know that he has in his possession thousands of documents which if published would impose crippling damage on the United States' surveillance capabilities and systems around the world. He has never done any of that," Greenwald told CNN.
An online petition calling on the White House to pardon Snowden passed the key threshold of 100,000 signatures over the weekend and had more than 110,000 early Monday.
The petition describes Snowden as "a national hero."
The White House says it will respond to any petition on its site that gathers more than 100,000 signatures in 30 days.