House Intelligence Committee Chairman Mike Rogers (R-Mich.) on Sunday urge the administration to keep up pressure on Russian President Vladimir Putin to hand over National Security Agency leaker Edward Snowden.

"If he were serious, he would send Mr. Snowden back to the United States," Rogers said, slamming Putin during in an interview with CNN's "State of the Union." "Not doing that, he's allowing this other game to play out, I really think, to try to help poke the U.S. in the eye."

Rogers' comments come as a number of countries this weekend offered asylum to Snowden, the man who revealed classified information about government surveillance programs. Snowden is believed to be hiding out in Moscow's airport, in hopes of evading an extradition order to the U.S., where he faces espionage charges.

Putin last month called Snowden a “free man,” and said Russia would not expel him from the country. But he expressed hope the standoff could be resolved quickly, with Snowden on his way out of Russia. 

Bolivian President Evo Morales on Sunday became the third Latin American leader to say Snowden would be welcome in his country, after Venezuela and Ecuador also granted him asylum. 

Rogers said he expects Snowden to go to Venezuela or Ecuador next. 

"So here you go, he is on this governments-who-oppress-their people tour. China, he's done Russia, now he'll do probably Venezuela, maybe Ecuador," Rogers continued. 

Snowden initially fled to Hong Kong after leaking the intelligence information, and then caught a flight to Russia.

"I do think the United States needs to take actions on this. We shouldn't just allow this to happen and shrug it off. This is serious business,” Rogers added. “Those Latin American [countries] enjoy certain trade benefits with the United States. We gotta look at all of them to send a very clear message that we won't put up with this kind of behavior."