"We're always concerned about Iran engaging in destabilizing activity around the globe," Obama told the station, WJAN America TeVe Miami. "But overall my sense is that what Mr. Chavez has done over the past several years has not had a serious national security impact on us."
Romney, seeking an edge both on national security and with Hispanic voters, said Obama's assertion was "misguided and misdirected."
"The idea that this nation, this president, doesn't pose a national security threat is simply naive and an extraordinary admission on the part of this president to be completely out of touch with what is happening in Latin America," Romney said of Chavez in an interview Wednesday with Fox News.
Obama said the US remains "vigilant" about Venezuela. But he said his main concern was making sure "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."
Chavez, who has been battling cancer, has close ties with Iran and has hosted Iranian leaders in Venezuela. He is seeking re-election and says he is cancer-free.
Chavez is roundly hated by many Venezuelans living in the U.S because of his crackdown on private enterprise, free speech and political opposition. The number of Venezuelans who now call the U.S. home — many are from the country's middle and upper class — has doubled in the past decade to 238,000, according to US Census figures.
More than half of them live in Florida, a key swing state in the Nov. 6 presidential election, and have a strong voice there despite making up less than 1 percent of Hispanics nationwide.
Any perception that Obama is failing to take Chavez seriously also could energize Florida's more conservative and politically powerful Cuban-Americans. Many of them also regard Chavez with disdain because of his close ties to former Cuban leader Fidel Castro and his financial support for the struggling Cuban government.
Obama campaign spokesman Ben LaBolt said Chavez is an attention-seeker and Romney played right into his hands.
"Hugo Chavez has become increasingly marginalized and his influence has waned," LaBolt said. "It's baffling that Mitt Romney is so scared of a leader like Chavez whose power is fading, while Romney continues to remain silent about how to confront al-Qaida or how to bring our troops home from Afghanistan."
Associated Press writer Laura Wides-Muñoz in Miami contributed to this report.