Clinton also expressed concern about democratically-elected leaders in Latin America who later move to undermine democratic institutions.
Clinton's remarks at a State Department public policy forum on Latin America were some of the strongest by an Obama administration official to date about increasing Iranian activity in the region.
Iran has been establishing close political, trade and other relationships with several Latin American governments, underlined by recent visits by Iranian President Mahmoud Ahmadinejad to Brazil, Venezuela and Bolivia.
In a question and answer session with participants in the event, Clinton said the United States has "no problem" with non-Western Hemisphere countries like China having legitimate business and investment activities in Latin America.
But she said US officials are concerned about what she said was Iran's "interest in promoting itself" in countries like Venezuela and Bolivia and said allowing Iranian influence to take root is, in her words, "a very bad idea for the countries involved."
"We hope that there will be recognition that this is the major supporter, promoter and exporter of terrorism in the world today," she said. "The Revolutionary Guard of Iran is increasing its control over the country because of the elections, which were a stark example of the abuse of human rights in action, is deeply involved in the economy as well as the security issues of Iran.
And I think that if people want to flirt with Iran, they should take a look at what the consequences might well be for them. And we hope that they will think twice and we're going to support them if they do."
There have been similar expressions of concern from Pentagon officials including Defense Secretary Robert Gates who in Senate testimony earlier this year said he was concerned about Iranian "meddling" in Latin America.
US officials have accused Iran of supporting activities in Latin America of the Lebanese militant group Hezbollah, and Tehran is accused of involvement in the nineties bomb attacks on a Jewish center and the Israeli embassy in Buenos Aires.
In the policy forum, Clinton also reiterated US "worry" about countries in Latin America where leaders who, after being democratically elected, move to undermine constitutional rule, citing in particular Venezuela and Nicaragua.
"We need to make it absolutely an article of faith that any leader elected must not just further his own position, and his power base, but respect the right of the people who elected him and build up the democracy so that democratic development and economic development can go hand in hand," she said.
Clinton said she hoped to see, "in the not-too-distant future," a democratic Cuba, which she said would be extraordinarily positive for the Hemisphere.
Mercopress