(CNN) – Any country that offers asylum to NSA leaker Edward Snowden pits itself against the United States, lawmakers from both parties agreed on Sunday.
Venezuela and Bolivia have extended asylum to Snowden, and Nicaragua has said it would consider it.
"It's very clear that any of these countries that accept Snowden and offer him political asylum is taking a step against the United States. It's making a very clear statement. I'm not surprised by the countries that are offering him asylum; they like sticking it to the United States," Sen. Robert Menendez, D-New Jersey, said on Sunday on NBC's "Meet the Press."
The chairman of the Senate Foreign Relations Committee suggested serious trade and policy implications for countries that accept Snowden.
"Clearly any such acceptance of Snowden to any country, any of these three or any other, is going to put them directly against the United States, and they need to know that," Menendez said.
Rep. Mike Rogers, chairman of the House Intelligence Committee agreed with Menendez, and he called for action from the United States.
"We shouldn't just allow this to happen and shrug it off. This is serious business. Those Latin American companies enjoy certain trade benefits with the United States. We ought to look at all of that to send a very clear message that we won't put up with this kind of behavior," the Michigan Republican told CNN's Candy Crowley Sunday on "The State of the Union."
Rogers said the countries willing to accept Snowden are using the former intelligence worker as a "public relations tool."
As Russian officials say Snowden remains in Moscow's Sheremetyevo International Airport, Sen. John McCain said President Vladimir Putin's unwillingness to turn over Snowden indicates the leader's dim view of the United States.
"It's clear what he is, is an old KGB colonel, and he's not interested in better relations with the United States. If he was, he would make sure that Mr. Snowden was sent back to us. We've got to have a much more realistic approach to Russia and Putin in order to comport with the realities of their relations with us," the Arizona Republican said on CBS' "Face the Nation."
While Venezuela has extended an offer for asylum, they are still waiting to see whether he accepts its offer, Foreign Affairs Minister Elias Jaua told state television Saturday.
Bill Richardson, former Democratic governor of New Mexico, said he doesn't understand Venezuela's offer of asylum considering the country's change in attitude toward the U.S. since the presidential elections earlier this year after the death of former President Hugo Chavez.
"What I don't understand: I was at the Venezuelan elections, and they want to improve the new, post-Chavez government, the relationship with the U.S. and they said that to me. I was an election observer - they have said that to the administration and now they say they are ready to take Snowden," the former U.S. ambassador to the United Nations said on CNN's "Newsroom."
"I hope Venezuela reverses itself. With Bolivia and Nicaragua, it's less so, but I think the U.S. has to pursue our interests and what Snowden did was unacceptable. You can't just decide you unilaterally to leak things. It's not loyalty to the United States," he added.
Snowden has revealed himself as the source of documents outlining a massive effort by the U.S. National Security Agency to track cell phone calls and monitor the e-mail and Internet traffic of almost all Americans.
CNN's Mariano Castillo contributed to this report.