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President Obama said in a Miami TV interview that Venezuelan President Hugo Chavez has not posed a "serious" security threat to the U.S., prompting a cascade of criticism from Mitt Romney and Republican lawmakers.

In an interview that aired Tuesday on the Spanish-language channel America TeVe, Obama discussed the Venezuelan leader when asked about his country's ties to Iran.

"We're always concerned about Iran engaging in destabilizing activity around the globe. But overall my sense is ... that what Mr. Chavez has done over the last several years has not had a serious national security impact on us," Obama said in response. "We have to be vigilant. My main concern when it comes to Venezuela is having the Venezuelan people have a voice in their affairs, and that you end up ultimately having fair and free elections, which we don't always see."

By Wednesday afternoon, several Republicans openly condemned the remark, with Romney calling it "stunning and shocking."

"The idea that this nation, that this president doesn't pose a national security threat to this country is simply naïve. It is an extraordinary admission on the part of this president to be completely out of touch with what's happening in Latin America," the GOP candidate told Fox News.

Romney, in a written statement, used the comment to build his claim that Obama's foreign policy has "emboldened adversaries and diminished U.S. influence in every region of the world," accusing the president of showing weakness on the world stage.

"Hugo Chavez has provided safe haven to drug kingpins, encouraged regional terrorist organizations that threaten our allies like Colombia, has strengthened military ties with Iran and helped it evade sanctions and has allowed a Hezbollah presence within his country's borders," Romney said in a written statement. "And he is seeking to lead -- together with the Castros -- a destabilizing, anti-democratic and anti-American 'Bolivarian Revolution' across Latin America."

The Republican presidential candidate was joined by several Florida lawmakers, whose constituents are known for their wariness toward Venezuela-aligned Cuba.

"The president appears to be blithely unaware of Chavez's hatred for our nation, including his efforts to promote anti-American regimes across the Western Hemisphere undermining our foreign and security policies," Rep. Ileana Ros-Lehtinen, R-Fla., chairwoman of the House Foreign Affairs Committee, said in a statement circulated by the Romney camp. The campaign sent around a similar statement from Rep. Connie Mack, R-Fla.

Earlier, Florida Republican Sen. Marco Rubio called Obama's comment "alarmingly naive."

"It's now disturbingly clear that President Obama has been living under a rock when it comes to recognizing the national security threat posed by Venezuela's Hugo Chavez," Rubio said in a statement.

He agreed that Chavez is a threat to freedom and democracy in Venezuela, but also noted he "supported Iran's regime in its attempts to expand its intelligence network throughout the hemisphere, facilitated money laundering activities that finance state sponsors of terrorism and provided a safe haven for FARC narco-terrorists."

The Socialist leader is in the midst of his own presidential campaign against Venezuelan opposition candidate Henrique Capriles. The South American country will hold the vote on Oct. 7. Chavez has been battling cancer for 13 months but told reporters at a press conference Tuesday that he is now completely "free" from the disease.

Fox News' Serafin Gomez contributed to this report.